{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "8e8d330f-b974-45ae-b563-29e44517133e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is a quick ipynb to reproduce Kenny-Imai Widespread Partisan Gerrymandering ... model\n"
     ]
    }
   ],
   "source": [
    "print(\"This is a quick ipynb to reproduce Kenny-Imai Widespread Partisan Gerrymandering ... model\")\n",
    "import numpy as np\n",
    "import math\n",
    "from scipy.stats import t, norm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "def r3(x):\n",
    "    return round(x,3)\n",
    "def r5(x):\n",
    "    return round(x,5)"
   ]
  },
  {
   "cell_type": "raw",
   "id": "e3a6a673-6fce-43a2-a3cd-1b6e7f86cd03",
   "metadata": {},
   "source": [
    "Kenny model:\n",
    "logit( vote share) = mean value + beta_t + eps_it\n",
    "beta_t is a national mean shift by election year with a global SD: Bt ~ N(x, sigmaB^2)\n",
    "eps_it is a student's t distribution: t_nu(0, sigmaE^2)\n",
    "sigmaB = 0.117\n",
    "sigmaE = 0.180\n",
    "nu = 2.896\n",
    "Example: GA-12.  At vGOP = 0.561, seat expectation = 0.83\n",
    "   At vGOP = 0.511, seat expectation = 0.59\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8800c20b-5243-43e1-9e0f-2f6e3587cb61",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "nu = 2.896\n",
    "sigmaB = 0.117\n",
    "sigmaE = 0.180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fd27dfef-56f8-4353-b960-46254e91a596",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here is the normal cumulative distribution vs. various t distributions with unit sd\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Here is the normal cumulative distribution vs. various t distributions with unit sd\")\n",
    "x = [-2 + 0.1*xx for xx in range(0,41)]\n",
    "nus = [1,2.896,5,10,20]\n",
    "for nu in nus:\n",
    "    y = [t.cdf(xx,nu,0,1) for xx in x]\n",
    "    plt.scatter(x,y,label=\"t \"+str(r3(nu)) )\n",
    "plt.plot(x, [norm.cdf(xx) for xx in x],label=\"normal,scale=1\")\n",
    "scal = 1.25\n",
    "plt.plot(x, [norm.cdf(xx,0,scal) for xx in x],label=\"normal \"+str(scal))\n",
    "plt.axhline(0.5,ls=\"--\")\n",
    "plt.axvline(0.,ls=\"--\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fa1eaa33-6085-4951-93ec-b2084480f135",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Let's show that logit is close to normal, but doesn't match Kenny GA-12 example\n",
      "sigmaB, sigmaE, nu, effective sigma 0.117 0.18 20 0.25360205046489664\n",
      "0.561 0.8332164607781047 0.6970346036955233 are v, logit, seat pairs\n",
      "0.511 0.5688818579103424 0.638505129686327 are v, logit, seat pairs\n",
      "Kenny-Imai has 56.1%, 83% and 51.1%, 59%\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Let's show that logit is close to normal, but doesn't match Kenny GA-12 example\")\n",
    "sd = (sigmaB**2 + (scal*sigmaE)**2)**0.5\n",
    "print(\"sigmaB, sigmaE, nu, effective sigma\",sigmaB, sigmaE, nu, sd)\n",
    "votes = [ 0.561, 0.511]\n",
    "for v in votes:\n",
    "    logit = norm.cdf(math.log(v/(1.-v)),0.,sd)\n",
    "    seat = math.exp(logit) / (1. + math.exp(logit))\n",
    "    print(v,logit, seat, \"are v, logit, seat pairs\")\n",
    "print(\"Kenny-Imai has 56.1%, 83% and 51.1%, 59%\")\n",
    "\n",
    "votes = [0.2 + 0.05*i for i in range(13)]\n",
    "logits = [norm.cdf(math.log(v/(1.-v)),0., sd) for v in votes]\n",
    "seats = [math.exp(logit) / (1. + math.exp(logit)) for logit in logits]\n",
    "plt.plot(votes,logits,label=\"logit\"+str(round(sd,3)))\n",
    "normSDs = [0.05, 0.06, 0.07]\n",
    "for normSD in normSDs:\n",
    "    normSeats = [norm.cdf(v,0.5,normSD) for v in votes]\n",
    "    plt.plot(votes,normSeats,label=\"norm\"+str(normSD) )\n",
    "plt.scatter([0.561,0.511],[0.83,0.59],marker=\"x\",label=\"GA-12\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8b20911a-17e7-4275-bd39-2b12a8541894",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24522149244752528\n"
     ]
    }
   ],
   "source": [
    "print(math.log(0.561/(1-0.561)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d34da7d4-8555-4de9-8323-f4ba81330564",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "nu = 2.896\n",
    "sigmaB = 0.117\n",
    "sigmaE = 0.180\n",
    "scal = 1.25\n",
    "\n",
    "sigmaE_app = sigmaE*scal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5868ddd4-6afc-4a29-bff5-8944163c996f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "showing that our piecewise convolution of pdf's works for simple case of adding two normal distros\n",
      "using sigmaB, nu, sigmaE of 0.117 2.896 0.18\n",
      "working on i= 0 out of 2000\n",
      "working on i= 200 out of 2000\n",
      "working on i= 400 out of 2000\n",
      "working on i= 600 out of 2000\n",
      "working on i= 800 out of 2000\n",
      "working on i= 1000 out of 2000\n",
      "working on i= 1200 out of 2000\n",
      "working on i= 1400 out of 2000\n",
      "working on i= 1600 out of 2000\n",
      "working on i= 1800 out of 2000\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABjM0lEQVR4nO3dd1xT5/4H8M8hbIQoU5DpwIWi4kJrW62j1tqhvWK1jtr21nu7rNe2Um9rawd2/uzS2+Fq66Aq2mVbqVtxgWBFcSEIahBBDXslz+8PJDUMJUg4GZ/365XXyzw5J/k+kuR880xJCCFAREREJBMbuQMgIiIi68ZkhIiIiGTFZISIiIhkxWSEiIiIZMVkhIiIiGTFZISIiIhkxWSEiIiIZMVkhIiIiGRlK3cAjaHVanHx4kW4urpCkiS5wyEiIqJGEEKgsLAQfn5+sLFpuP3DLJKRixcvIiAgQO4wiIiIqAmys7Ph7+/f4ONmkYy4uroCqK6Mm5ubzNEQERFRYxQUFCAgIEB3HW+IWSQjNV0zbm5uTEaIiIjMzK2GWHAAKxEREcmKyQgRERHJiskIERERycosxowQEVkbIQSqqqqg0WjkDoWoQQqFAra2tre97AaTESIiE1NRUQGVSoWSkhK5QyG6JWdnZ/j6+sLe3r7Jz2FwMrJr1y588MEHSEpKgkqlwsaNG/HQQw/d9Jzy8nIsWLAA33//PXJycuDv74958+ZhxowZTY2biMgiabVaZGRkQKFQwM/PD/b29lzskUySEAIVFRW4fPkyMjIy0KlTp5subHYzBicjxcXFCA8Px+OPP47x48c36pwJEybg0qVLWLp0KTp27Ijc3FxUVVUZHCwRkaWrqKiAVqtFQEAAnJ2d5Q6H6KacnJxgZ2eHc+fOoaKiAo6Ojk16HoOTkdGjR2P06NGNPv7333/Hzp07cfbsWbi7uwMAgoODDX1ZIiKr0tRfmEQtrTneq0Z/t//000/o27cv3n//fbRr1w6hoaGYM2cOSktLGzynvLwcBQUFejciIiKyTEZPRs6ePYs9e/YgNTUVGzduxKJFi7B+/Xo888wzDZ4TExMDpVKpu3FfGiIiag6ZmZmQJAkpKSmyvP4bb7yBXr16NfvzrlixAq1bt9Yr++qrrxAQEAAbGxssWrSo2V+zORk9GdFqtZAkCatWrUL//v1x33334eOPP8aKFSsabB2Jjo6GWq3W3bKzs40dJhHJRKUuRUJ6HlTqhltLieRkrATCmAoKCvDss8/ilVdewYULF/DPf/5T7pBuyuhTe319fdGuXTsolUpdWdeuXSGEwPnz59GpU6c65zg4OMDBwcHYoRGRzGIPZSE67ii0ArCRgJhxPRDVL1DusIjMXlZWFiorKzFmzBj4+vrKHc4tGb1lZPDgwbh48SKKiop0ZadOnYKNjc1NtxMmIsumUpfqEhEA0Arg1bhUtpCYMa1Wi/feew8dO3aEg4MDAgMD8c477+geP3r0KIYNGwYnJyd4eHjgn//8p961Yfr06XjooYfw4YcfwtfXFx4eHnjmmWdQWVkJoLrVfODAgXVet2fPnpg/f74uhgULFsDf3x8ODg7o1asXfv/99wZjrq97Y9OmTbrp1CtWrMCbb76JI0eOQJIkSJKEFStWAADUajX++c9/wtvbG25ubhg2bBiOHDmi91wLFy6Ej48PXF1d8cQTT6CsrOym/4c7duyAJEn49ddfER4eDkdHRwwYMABHjx6tE3dgYCCcnZ3x8MMPIz8/X++xHj16AADat28PSZKQmZl509eVm8HJSFFREVJSUnT9bRkZGUhJSUFWVhaA6jfL1KlTdcdPmjQJHh4eePzxx3H8+HHs2rULL730EmbMmAEnJ6fmqQURmaSbdcFk5BXrEpEaGiGQmVd3oS925ZiH6OhovPfee3jttddw/PhxrF69Gj4+PgCAkpIS3HvvvWjTpg0OHTqEdevW4c8//8Szzz6r9xzbt29Heno6tm/fjpUrV2LFihW6i//kyZNx4MABpKen644/duwYjh49ismTJwMAPvnkE3z00Uf48MMP8ddff2HUqFF44IEHcPr06SbVKSoqCv/5z3/QvXt3qFQqqFQqREVFQQiBMWPGICcnB5s3b0ZSUhL69OmDe+65B1euXAEA/PDDD5g/fz7eeecdJCYmwtfXF4sXL27U67700kv48MMPcejQIXh7e+OBBx7QJWUHDhzAjBkz8O9//xspKSkYOnQo3n77bb2Y//zzTwDAwYMHoVKpTH/spTDQ9u3bBYA6t2nTpgkhhJg2bZq466679M5JS0sTw4cPF05OTsLf31/Mnj1blJSUNPo11Wq1ACDUarWh4RKRTNYePCdC5v4igl75RYTM/UWsOZApzuQWiu/2ZYp5G/8S4xbvEUGv/FLnNnfDEbH5r4sir7Cs3udZe/CczDUzrtLSUnH8+HFRWlraLM938VqJ2Hvmsrh4rfHfuU1RUFAgHBwcxNdff13v41999ZVo06aNKCoq0pX9+uuvwsbGRuTk5Aghqq8fQUFBoqqqSnfMP/7xDxEVFaW737NnT7FgwQLd/ejoaNGvXz/dfT8/P/HOO+/ovXa/fv3Ev//9byGEEBkZGQKASE5OFkIIsXz5cqFUKvWO37hxo7jx8jh//nwRHh6ud8zWrVuFm5ubKCsr0yvv0KGD+PLLL4UQQkRGRoqZM2fqPT5gwIA6z3Wjmmvs2rVrdWX5+fnCyclJxMbGCiGEePTRR8W9996rd15UVJRePZKTkwUAkZGR0eBrNZebvWcbe/02eMzI3XffDSFEg4/XZLA36tKlC+Lj4w19KSIyU/V1wcyNS23UuWsOZmPNwepB6+H+Svx1Xo2ab5yarpw7Q73gq2TL6q205JictLQ0lJeX45577mnw8fDwcLi4uOjKBg8eDK1Wi5MnT+paULp37w6FQqE7xtfXV6+LYvLkyVi2bBlee+01CCGwZs0azJo1C0D1oM2LFy9i8ODBeq89ePDgOt0ntyspKQlFRUXw8PDQKy8tLdW13KSlpWHmzJl6j0dGRmL79u23fP7IyEjdv93d3dG5c2ekpaXpnvfhhx+uc/zNuqNMHfemIaJmV18XDADY2kjoH+KOnv6t0bltK3i1ckRZlQbnr5TCzckWxeVVOHWpCIcyr+BETiGOnFfXeY6arhwmIzfX0JgcYyVyt+p2F0I0uKz9jeV2dnZ1HtNqtbr7kyZNwty5c3H48GGUlpYiOzsbEydObPD5bvXaNjY2dX5g13SH3IxWq4Wvry927NhR57HaY1CaS00dbtYgYK6YjBBRs7pUUIblezLqlEsA/nhxCDp4uTbqeXLUZfj+wDl8vu1Mnedp16ZpS05bk5uNyTFGMtKpUyc4OTlh69atePLJJ+s83q1bN6xcuRLFxcW61pG9e/fCxsYGoaGhjX4df39/3HnnnVi1ahVKS0sxfPhwXauKm5sb/Pz8sGfPHtx55526cxISEtC/f/96n8/LywuFhYV6cdVeg8Te3r7O7sl9+vRBTk4ObG1tG1xVvGvXrti/f7/eOMr9+/c3qp779+9HYGB1K9bVq1dx6tQpdOnSBUD1/2Xt52ns85oqrjdMRM1CqxX4bv85DP9oJ+LTcgFUJw4AoJAkLBzfo9GJCAC0VTpizsjOiBkXpvdFJQBMX34IKdnXmit0ixTi6QKbWo0BCklCsKdx9rtxdHTEK6+8gpdffhnffvst0tPTsX//fixduhRAdfeKo6Mjpk2bhtTUVGzfvh3PPfccpkyZoksmGmvy5MlYu3Yt1q1bh8cee0zvsZdeegnvvfceYmNjcfLkScydOxcpKSl44YUX6n2uAQMGwNnZGa+++irOnDmD1atX1xluEBwcrJuskZeXh/LycgwfPhyRkZF46KGH8McffyAzMxMJCQn473//i8TERADACy+8gGXLlmHZsmU4deoU5s+fj2PHjjWqjgsWLMDWrVuRmpqK6dOnw9PTU7cp7fPPP4/ff/8d77//Pk6dOoXPP//crLtoABg+gFUOHMBKZHpuHBiZX1Qupi87oBuE+sDne8TR89fExWslIuFM3m0Pnrx4rUTsOX1ZfL0rXUS8FS+CXvlFtI/+VSyKPyUqqzR14jFnzTmAde3Bc6L93F+r/7/m/mr0wb8ajUa8/fbbIigoSNjZ2YnAwEDx7rvv6h7/66+/xNChQ4Wjo6Nwd3cXTz31lCgsLNQ9Pm3aNPHggw/qPecLL7xQZ1LE1atXhYODg3B2dtY7vyaGN998U7Rr107Y2dmJ8PBw8dtvv+kerz2AVYjqAasdO3YUjo6O4v777xdfffWV3gDWsrIyMX78eNG6dWsBQCxfvlwIUT1o97nnnhN+fn7Czs5OBAQEiMmTJ4usrCzdue+8847w9PQUrVq1EtOmTRMvv/xyowaw/vzzz6J79+7C3t5e9OvXT6SkpOgdt3TpUuHv7y+cnJzE2LFjxYcffmjWA1glIUy/86mgoABKpRJqtRpubm5yh0Nk9W4cGCkBcHOyg7q0Eg62Noge3QVTIoOhqP2zvJmoSyrx2o+p+OnIRQDAkE6eGNbFG2/9ctwiFk8rKytDRkYGQkJCmrwD6o1U6lJk5pUg2NOZ42zMwI4dOzB06FBcvXrVaGNPmtvN3rONvX5zzAgRGaT2wEgBQF1aiUB3Z3w5JQJdfY37g0HpbIdPH+2NYV28ER13FLtP52H36Tzd45xxo89X6cT/BzJ5HDNCRAZpaKbMG2O7Gz0RudFDvdthw78GwbOVfZ3HGlo8jYhME5MRIjJIsEfdAZA2ALr6NX5wanPp5ueGb5+oO0vCmAM1iYypZi0vc+miaS5MRoio0YQQ+H5/ll6ZDYCY8T1k6wro5qvEgge76ZU9PjiYXRNEZoRjRoio0T6OP4XFO6pXl5w1vBMGhHiYxMDIqZEhuDPUC//54S8knbuKVQeycG9YW/QNdpc1LiJqHLaMEFGjrEzIxGfXFyCbP7YbZg0PRWQHD9kTkRrBHq2w+qkBGNLJE6WVGjy+/BBSL9RdwZWITA+TESK6pd+OqvDGz9WLNc0ZGYrHB4fIHFH9HGwV+GpKX/QPdkdheRUeX3EIF69xp18iU8dkhIhuKjHzCl6ITYEQwGMDA/HM0I5yh3RTTvYKLJ3eF519XHG5sBwzVhxCUXmV3GER0U0wGSGiOlTqUiSk5+FI9lXM/D4JFVVajOjmgzcfCGtwwzFT4upoh6XT+8KzlQNO5BTiudWHUaXR6uqlUrO1hMiUMBkhIj2xh7IweOE2TPr6AB78IgF5RRXo0tYVn0zsZbRVVY3Bv40zvpnWF452Nth+8jKe/DZRV6/BC7ch9lDWrZ+EyETt2LEDkiTh2rVrzfq8mZmZkCRJb7PAvXv3okePHrCzs9Ptj9PcmIwQkU7t1VVrvP1QGJztzW/yXa+A1vjgkXAAwI6Tl3X1qlmllS0kzevuu+/GrFmzZHv9yspKvPLKK+jRowdcXFzg5+eHqVOn4uLFi7LFZAlmz56NXr16ISMjo84mgs2FyQgR6TS0umqlxuS3sGrQ2HA/jOped1dYrtIqDyEEqqqMM4anpKQEhw8fxmuvvYbDhw8jLi4Op06dwgMPPGCU17uViooKWV63uaWnp2PYsGHw9/c32mJsTEaISCfE0wW1O2IsYTXTeWO61imzhHqZkunTp2Pnzp345JNPIEkSJElCZmamrjvhjz/+QN++feHg4IDdu3dj+vTpdZr8Z82ahbvvvlt3XwiB999/H+3bt4eTkxPCw8Oxfv36BmNQKpWIj4/HhAkT0LlzZwwcOBCfffYZkpKSkJXVcLdcTddEXFwchg4dCmdnZ4SHh2Pfvn16x23YsAHdu3eHg4MDgoOD8dFHH+k9HhwcjLfffhvTp0+HUqnEU089hRUrVqB169b45Zdf0LlzZzg7O+ORRx5BcXExVq5cieDgYLRp0wbPPfccNBqN7rm+//579O3bF66urmjbti0mTZqE3NzcRvwl/iZJEpYsWYLRo0fDyckJISEhWLdund4xBw8eRO/eveHo6Ii+ffsiOTm5zv9Lfn4+ZsyYAUmS2DJCRMbXxtkebZV/77ppA+DdcWEms5ZIUwW6uyB6dBfdfQnmVS8hBEoqqmS5NXZj908++QSRkZF46qmnoFKpoFKpEBAQoHv85ZdfRkxMDNLS0tCzZ89GPed///tfLF++HEuWLMGxY8fw4osv4rHHHsPOnTsb/X+nVqshSVKjftHPmzcPc+bMQUpKCkJDQ/Hoo4/qWnGSkpIwYcIETJw4EUePHsUbb7yB1157rc7F+YMPPkBYWBiSkpLw2muvAahusfn000+xdu1a/P7779ixYwfGjRuHzZs3Y/Pmzfjuu+/w1Vdf6SVaFRUVeOutt3DkyBFs2rQJGRkZmD59eqPrXeO1117D+PHjceTIETz22GN49NFHkZaWBgAoLi7G/fffj86dOyMpKQlvvPEG5syZozs3ICAAKpUKbm5uWLRoEVQqFaKiogyOoTHMrxOYiIxm4W8noFKXoY2zHd59uAd6BbY2mwv2rTx9Vwe0cbHDy+uPAgAC2phPq0hppQbdXv9Dltc+vmBUo8YLKZVK2Nvbw9nZGW3btq3z+IIFCzBixIhGv25xcTE+/vhjbNu2DZGRkQCA9u3bY8+ePfjyyy9x11133fI5ysrKMHfuXEyaNOmm29fXmDNnDsaMGQMAePPNN9G9e3ecOXMGXbp0wccff4x77rlHl2CEhobi+PHj+OCDD/SShGHDhuld0Pfs2YPKykosWbIEHTp0AAA88sgj+O6773Dp0iW0atUK3bp1w9ChQ7F9+3bdxX7GjBm652jfvj0+/fRT9O/fH0VFRWjVqtUt61LjH//4B5588kkAwFtvvYX4+Hh89tlnWLx4MVatWgWNRoNly5bB2dkZ3bt3x/nz5/Gvf/0LAKBQKNC2bVtIkgSlUlnv37W5sGWEiAAAO07mYkVCJgDg4wm9MLqHr8UkIjUm9A3Eo/0DIQD8Z90RqEsq5Q7JavTt29eg448fP46ysjKMGDECrVq10t2+/fZbpKen3/L8yspKTJw4EVqtFosXL9aVz5w5U+/5bnRji42vry8A6LpG0tLSMHjwYL3jBw8ejNOnT+t1r9RXT2dnZ10iAgA+Pj4IDg7We30fHx+9bpjk5GQ8+OCDCAoKgqurq6776mbdTfWpSeRuvF/TMpKWlobw8HA4Ozs3eHxLYcsIEaGgrBJzN1S3GEwfFIyhXbxljsh4Xru/K/afzUdGXjHmbTqKzyf1kTukW3KyU+D4glGyvXZzcHFx0btvY2NTpwuosvLv5FCr1QIAfv31V7Rr107vOAcHh5u+VmVlJSZMmICMjAxs27ZNr1VkwYIFei0XN7Kzs9P9u2Y9nZo4hBB11tiprwurdj1rP2/Nc9dXVvNaxcXFGDlyJEaOHInvv/8eXl5eyMrKwqhRo5plUGxNPRrbBdcSmIwQEd79NQ05BWUI9nDGK/d2ufUJZszZ3haLonph3JIE/PKXCvf3zMG9YcZrfm4OkiSZxdRqe3t7vVaCm/Hy8kJqaqpeWUpKiu4i3a1bNzg4OCArK6tRXTI1ahKR06dPY/v27fDw8NB73NvbG97ehifb3bp1w549e/TKEhISEBoaCoWieRK2GidOnEBeXh4WLlyoG3eTmJjYpOfav38/pk6dqne/d+/eAKrr9N1336G0tBROTk66x+XAbhoiK7fr1GWsPZQNAHhvfE842TfvF6spCg9ojZl3tQcAvP5jKtSl7K5pDsHBwThw4AAyMzORl5en+6Vfn2HDhiExMRHffvstTp8+jfnz5+slJ66urpgzZw5efPFFrFy5Eunp6UhOTsYXX3yBlStX1vucVVVVeOSRR5CYmKgbD5GTk4OcnJzbblH4z3/+g61bt+Ktt97CqVOnsHLlSnz++ecNtrLcjsDAQNjb2+Ozzz7D2bNn8dNPP+Gtt95q0nOtW7cOy5Ytw6lTpzB//nwcPHgQzz77LABg0qRJsLGxwRNPPIHjx49j8+bN+PDDD5uzKo3GZITIihWVVyE67u/umQHtPW5xhuV4blgntPdyQW5hOWI2p8kdjkWYM2cOFAoFunXrputaaMioUaPw2muv4eWXX0a/fv1QWFio9wseqB5w+frrryMmJgZdu3bFqFGj8PPPPyMkpP6NGs+fP4+ffvoJ58+fR69eveDr66u7JSQk3Fbd+vTpgx9++AFr165FWFgYXn/9dSxYsKBJM1xuxcvLCytWrMC6devQrVs3LFy4sMlJwptvvom1a9eiZ8+eWLlyJVatWoVu3boBAFq1aoWff/4Zx48fR+/evTFv3jy89957zVmVRpOEKXUaNaCgoABKpRJqtbpRI6KJqHHm/5iKlfvOIcDdCX/MutMsugKa08GMK5jwZfVaEqufGoBBHTxljqh6BkhGRgZCQkLg6Oh46xOIGiBJEjZu3Gi0Jdxr3Ow929jrN1tGiKzU0fNqfLf/HAAg5uGeVpeIAED/EHc8NjAQABAddxRllY0b70BEzYvJCJGVUalLsefMZbyy4S9oBfBAuB/u6CR/i4BcXrm3C3yVjjiXX4IlO9K5sy+RDKzvpxCRFYs9lKW3EZ6DrQ3+W89S6dbE1dEO/x3TDc+sPowvtp/Bp1tPQwCwkYCYcT0Q1S9Q7hCJmsQMRmHosGWEyErUtyNvRZUWGjP6wjKW+3q0RURQG1RpBWr+N7izL1HLYTJCZCXq25FXANy5FtUD/aL6+dcp586+RC2DyQiRlbDUHXmby5BOXnXK5Pz/MacmdrJuzfFeNTgZ2bVrF8aOHQs/Pz9IkoRNmzY1+ty9e/fC1tYWvXr1MvRlieg2tXVzRLDn30tVKyTJrHauNTZfpRPefKCb7r5cO/vWrEBaUsIWGTIPNe/V2kvcG8LgAazFxcUIDw/H448/jvHjxzf6PLVajalTp+Kee+7BpUuXDH1ZIrpNfxy7hIy8Ytjb2uDjf4QjIrgNE5Fapg0KQZVW4K1f0uBkr8Dwrj4tHoNCoUDr1q11m6Y5OzvX2ROFyBQIIVBSUoLc3Fy0bt36tpbFNzgZGT16NEaPHm3wCz399NOYNGkSFAqFQa0pRHT7Kqq0WPhb9SqjT9/ZHveH+8kckel6fFAI4g5fwLGLBfh062m8+WBYi8dQs1X7jbu4Epmq1q1b696zTdUiU3uXL1+O9PR0fP/993j77bdveXx5eTnKy8t19wsKCowZHpHF+27/OWTml8DL1QEz7+pw6xOsmI2NhHn3dcWkbw5g1YEsTBsUjPZerW59YjOSJAm+vr7w9vbW28mWyNTY2dk1y0aBRk9GTp8+jblz52L37t2wtW3cy8XExODNN980cmRE1uFaSQU+3XoaADBnZChcHLi80K0M6uiJoZ29sP3kZbz3+wl8OaWvLHEoFIpm3xGWyBQZdTaNRqPBpEmT8OabbyI0NLTR50VHR0OtVutu2dnZRoySyLJ9tu0M1KWV6NLWFY9EBMgdjtmIvq8rbKTqsTaHMq/IHQ6RRTNqMlJYWIjExEQ8++yzsLW1ha2tLRYsWIAjR47A1tYW27Ztq/c8BwcHuLm56d2IyHAXr5Xq9p+Jvq8rFDYcCNlYoT6uiOpXnby982sap9oSGZFR22vd3Nxw9OhRvbLFixdj27ZtWL9+fYPbQBNR8/hs22lUVGkxIMQdd1rx/jNN9eLwUPyYchEp2dew5fgljOp+e4P0iKh+BicjRUVFOHPmjO5+RkYGUlJS4O7ujsDAQERHR+PChQv49ttvYWNjg7Aw/ZHo3t7ecHR0rFNORM0rI68YPySeBwC8NKozp4c2gbebI2YMDsHn28/g4y2nMKKrD2zYukTU7AzupklMTETv3r3Ru3dvAMDs2bPRu3dvvP766wAAlUqFrKys5o2SiAz2f/GnoNEKDOvijb7B7nKHY7aeGtIero62OHmpEL8cVckdDpFFkoQZdIQWFBRAqVRCrVZz/AhRIxy/WID7Pt0NAPj1+TvQ3U8pc0Tm7bOtp/FR/Cm093TBlhfvhK2CO2kQNUZjr9/8RBFZoI/jTwIA7u/py0SkGTx+RwjaONvhbF4xNiZfkDscIovDZITIwhzOuoo/03KhsJEwe0Tjp9RTw1o52OJfd1cvFvfJ1upBwUTUfJiMEFkQlboUb/50DAAwvk+7Fl851JJNGRgML1cHnL9aiq93n0VCeh5U6lK5wyKyCFyKkchCxB7KwtwNR1EzCCzYw+Wmx5NhnOwVeHZoR8z/6Rg++KO6G8xGAmLG9UBUv0CZoyMyb2wZIbIAKnUpouP+TkQA4KMtp/jLvZnd3dlL775WAK/GpfL/meg2MRkhsgAZecXQ1poXpxECmXkl8gRkoS5cq5t08P+Z6PYxGSGyACGedbtkFJKEYE9nGaKxXCGeLqi95Bn/n4luH5MRIgugLtXfZl4hSXh3XBh8lU4yRWSZfJVOWDi+h15C8vbD3fn/THSbOICVyAJ8tq16i4Z7unrjyTvaI9jTmRdII4nqF4iIoDZ46IsEFJVXwcXBTu6QiMweW0aIzNyZ3EJsvr5M+UujOiOygwcTESPr6O2Kf97ZHgDwxbYz0NYesENEBmEyQmTmluw4CyGAUd190KUtt0toKdMGBcPVoXrPmvi0S3KHQ2TWmIwQmbGL10rxY0r18uT/vrujzNFYF6WTHaYOCgIAfL7tDMxgmy8ik8VkhMiMLd2TgSqtQGR7D4QHtJY7HKszY3AInOwUOHpBjYT0fLnDITJbTEaIzJS6pBJrDmYBAJ6+q73M0Vgnj1YOmNDXHwDwv53pMkdDZL6YjBCZqe/2Z6KkQoOuvm64K9Tr1ieQUTw5pD1sJGD36Twcv1ggdzhEZonJCJEZKqvUYPneTADAzLvaQ5JqL8VFLSXA3Rn39fAFAHy9+6zM0RCZJyYjRGZofdJ55BdXoF1rJ4y5fiEk+Tx9ZwcAwE9HLta7ZDwR3RyTESIzo9EK3S/wp4aEwFbBj7HcevgrEdneAxqtwLI9GXKHQ2R2+C1GZGZ+S1XhXH4J2jjbYUK/ALnDoetqBhGvPZhVZ3l+Iro5JiNEZkQIgS93VreKTI0MhrM9d3QwFXeFeqFLW1cUV2iw6sA5ucMhMitMRojMyMGMKzh6QQ1HOxtMGxQsdzh0A0mS8NSQ6taR5XszUV6lkTkiIvPBZITITKjUpfhwy0kAwLg+/nB3sZc5IqptbLgffJWOuFxYjhUJmUhIz4NKzQGtRLfCNl4iMxB7KAtzNxxFzYLjbd0cZI2H6mdva4PHBwfj3c0nELP5BADARgJixvVAVL9AmaMjMl1sGSEycSp1KaLj/k5EAOCTP8/wF7eJuruz/gJ0WgG8GpfKvxfRTTAZITJxGXnFqL1DvUYIZOaVyBMQ3VReUUWdMv69iG6OyQiRiQvxdEHt9VUVkoRgT2dZ4qGb49+LyHBMRohMnLerI9o42+nuKyQJ744Lg6/SScaoqCG+SicsHN9Dd18C+PciugUOYCUycfHHL+FKSSXcHG3x6aO90bmtKy9sJi6qXyAc7RR4YW0KnOwVGM0l+4luii0jRCZu2d7q5cUfGxiEuzt7MxExEw+E+6GTdyuUVGjww6FsucMhMmlMRohMWOoFNQ5mXIGtjYSpkcFyh0MGkCQJjw8OAQCs3JcJTe1RyESkw2SEyITVbLo2pqcv2iodZY6GDPVw73Zo7WyH7Cul+DPtktzhEJksg5ORXbt2YezYsfDz84MkSdi0adNNj4+Li8OIESPg5eUFNzc3REZG4o8//mhqvERWI7ewDD//dREA8MQdITJHQ03hZK/ApP7Vi50t38vdfIkaYnAyUlxcjPDwcHz++eeNOn7Xrl0YMWIENm/ejKSkJAwdOhRjx45FcnKywcESWZM1B7JRqRHoE9gaPf1byx0ONdGUyCAobCTsP3sFxy6q5Q6HyCQZPJtm9OjRGD16dKOPX7Rokd79d999Fz/++CN+/vln9O7d29CXJ7IKlRotVh+s3vmVG+KZN1+lE+7r4Yufj1zEyoRMvP9IuNwhEZmcFh8zotVqUVhYCHd39waPKS8vR0FBgd6NyJrEH7+ESwXl8Gxlj3vD2sodDt2maZFBAIAfUy5CXVIpczREpqfFk5GPPvoIxcXFmDBhQoPHxMTEQKlU6m4BAQEtGCGR/L7dlwkAeLR/IBxsFfIGQ7ctIqgNuvq6obxKi3VJnOZLVFuLJiNr1qzBG2+8gdjYWHh7ezd4XHR0NNRqte6Wnc0PL1mPkzmF2H/2ChQ2EiYN4E6vlkCSJEy93jry3f5z0HKaL5GeFktGYmNj8cQTT+CHH37A8OHDb3qsg4MD3Nzc9G5E1uK7/ZkAgBFdfbjAmQV5sJcfXB1tcS6/BLtOX5Y7HCKT0iLJyJo1azB9+nSsXr0aY8aMaYmXJDJLhWWV2Hj4AgDofkmTZXC2t8U/Iqq7nL/bd07maIhMi8HJSFFREVJSUpCSkgIAyMjIQEpKCrKysgBUd7FMnTpVd/yaNWswdepUfPTRRxg4cCBycnKQk5MDtZpT3Ihqizt8AcUVGnT0boXIDh5yh0PN7LGB1d1u207mIvtKiczREJkOg5ORxMRE9O7dWzctd/bs2ejduzdef/11AIBKpdIlJgDw5ZdfoqqqCs888wx8fX11txdeeKGZqkBkGYQQuoGrUyODIEm1N6Inc9feqxWGdPKEEMD3B9g6QlRDEkKY/EiqgoICKJVKqNVqjh8hi7X3TB4mf3MALvYK7H/1Hrg62skdEhnBlmM5+Od3SWjjbId90ffA0Y6zpchyNfb6zb1piExETavIuD7+TEQs2D1dfdCutROullTi179UcodDZBKYjBCZgOSsq9hyvHojNQ5ctWw3TtleuicDCel5UKlLZY6KSF5MRohkFnsoCw8vTkBNh+nhrKvyBkRGN7FfABQ2Eo6rCjDp6wMYvHAbYg9l3fpEIgvFZIRIRip1KeZuOKpX9mpcKn8pW7gKjRaaGxY+0wr+3cm6MRkhklFGXjFqjyDXCIHMPE77tGQZecV1yvh3J2vGZIRIRiGeLnXKFJKEYE9nGaKhlhLi6YLaE7f5dydrxmSESEaVVfrtIgpJwrvjwrgMvIXzVTph4fgeegnJOw9359+drJat3AEQWbO11wctDghxx6zhoQj2dOYFyUpE9QtERFAb3P/ZHpRVahHs2UrukIhkw5YRIplUarRYl3QeADB9UDAiO3gwEbEyHb1d8XBvfwDAqgOcTUPWi8kIkUy2puXicmE5PFs5YHg3H7nDIZlMvr7myO+pKuQXlcscDZE8mIwQyaSmi+aRCH/YKfhRtFZh7ZTo6a9EpUZg/fWWMiJrw29AIhmcv1qCnacuA6heAIusW03ryJqDWdBqTX67MKJmx2SESAY/JJ6HEMCgDh4Irmd6L1mXseF+cHWwRWZ+CfadzZc7HKIWx2SEqIVVabT44VA2AODR/oEyR0OmwNneFg/1bgcAWM2BrGSFmIwQtbCdpy4jp6AMbZztMLI7B65StZrN8/44loPLhRzIStaFyQhRC1tzsPqX7/g+/nCwVcgcDZmKrr5u6B3YGlVagXVJ2XKHQ9SimIwQtaAcdRm2ncgFAExkFw3VMqk/B7KSdWIyQtSCfkjMhlYA/YPd0dGbK26Svvt7+sHV0RbZV0qx+0ye3OEQtRgmI0QtRKMViK0ZuDqA03mpLid7Bcb3qV6RdfWBczJHQ9RymIwQtZDdpy/jwrVSuDnaYnSYr9zhkImqGcj6Z1ouLhWUyRwNUctgMkLUQtYerG4VGdfHH452HLhK9Qv1cUXfoDbQaIVuCjiRpWMyQtQCcgvL8GfaJQBcW4RubfLA6vfI2kPZ0HAgK1kBJiNELWB90nlUaQX6BLZG57aucodDJm50mC9aO9vhwrVS7Dp9We5wiIyOyQiRkV24VoIVezMBcDovNY6jnQIPX1+RdcXeTCSk50GlLpU5KiLjYTJCZESxh7Jwx8LtyL2+omZ5pUbmiMhcTOxXnbjuPHUZk74+gMELtyH2EJeKJ8vEZITISFTqUkTHHcWNPf5v/HScv3CpUdycbPXuawXwalwq3z9kkZiMEBlJRl4xao891AiBzLwSeQIis5KRV1ynjO8fslRMRoiMJMTTBVKtMoUkIdjTWZZ4yLzw/UPWhMkIkZG0dXOERyt73X2FJOHdcWHwVTrJGBWZC1+lExaO76FLSCSA7x+yWLa3PoSImuJAxhXkFVXAyU6BLyb1QVc/V15IyCBR/QLh5eqAGSsSYaewwajubeUOicgo2DJCZCRrD1bPfHiotx+GdfVmIkJNMrSzN7r5uqFCo8XG5Atyh0NkFExGiIzgWkkFNqfmAPh7iiZRU0iShIn9qzdWXHswG0JwRVayPAYnI7t27cLYsWPh5+cHSZKwadOmW56zc+dOREREwNHREe3bt8f//ve/psRKZDbiDl9ARZUW3Xzd0NNfKXc4ZOYe7NUOjnY2OHmpEMnZ1+QOh6jZGZyMFBcXIzw8HJ9//nmjjs/IyMB9992HIUOGIDk5Ga+++iqef/55bNiwweBgicyBEAJrry9O9Wj/AEhS7TkRRIZROtnhvh7VOz3HHuTmeWR5DB7AOnr0aIwePbrRx//vf/9DYGAgFi1aBADo2rUrEhMT8eGHH2L8+PGGvjyRyTucdRWnLhXB0c4GD15f0pvodk3sF4i4wxfw818X8drYbmjlwPkHZDmMPmZk3759GDlypF7ZqFGjkJiYiMrKynrPKS8vR0FBgd6NyFysuf7L9f6efnBztJM5GrIU/YLboIOXC0oqNPgp5aLc4RA1K6MnIzk5OfDx8dEr8/HxQVVVFfLy8uo9JyYmBkqlUncLCAgwdphEzUJdWolf/qq+UDzan+9baj6SJOkGQ3OPGrI0LTKbpnafec1o8Ib60qOjo6FWq3W37Gz2kZJ5+CnlAsoqtQj1aYU+gW3kDocszLg+7WCnkHDkvBrHL7LFmCyH0ZORtm3bIicnR68sNzcXtra28PDwqPccBwcHuLm56d2ITJ0QAquvd9FM7BfIgavU7DxaOWBkt+qFz9aydYQsiNGTkcjISMTHx+uVbdmyBX379oWdHfvTyXL8dV6NNFUB7G1tMK4PB66ScdSsObIx+QLKKjUyR0PUPAxORoqKipCSkoKUlBQA1VN3U1JSkJVVnaVHR0dj6tSpuuNnzpyJc+fOYfbs2UhLS8OyZcuwdOlSzJkzp3lqQGQi1lxfcfW+sLZo7Wx/i6OJmmZwB0/4t3FCYVkVNh9VyR0OUbMwOBlJTExE79690bt3bwDA7Nmz0bt3b7z++usAAJVKpUtMACAkJASbN2/Gjh070KtXL7z11lv49NNPOa2XLEpReRV+OlIzcJUrrpLx2NhIiOr794qsRJZAEmawtnBBQQGUSiXUajXHj5BJWn0gC69uPIr2Xi7YOvsujhcho8pRl2HQwq3QCmDrf+5CB69WcodEVK/GXr+5Nw1RM9CtuMqBq9QC2iodMbSzNwAg9hBbR8j8MRkhuk2pF9T467wadgqJA1epxUy83h24Iek8Kqq0MkdDdHuYjBDdpppWkVHd28KjlYPM0ZC1GNrZC96uDsgvrsCfaZfkDofotjAZIboNZy8XYUPSeQAcuEoty1Zhg3/09QcArEzIREJ6HlTqUpmjImoaJiNETRR7KAv3fLQTpZXVTeRZV4pljoisTVTf6gT4QMYVTPr6AAYv3Mal4sksMRkhagKVuhTRcUdx41S0/248xl+m1KLsbPUHS2sF8GpcKt+HZHaYjBA1QUZeMbS1JsVrhEBmXok8AZFVysir2xrH9yGZIyYjRE0Q4ulSp0whSQj2dJYhGrJWIZ4uqD2RnO9DMkdMRoiaoI2zPZzs/v74KCQJ744Lg6/SScaoyNr4Kp2wcHwPvYSE70MyR7ZyB0BkjjYfVaG0Uou2Skd89I9wtPdy4QWAZBHVLxCB7s549OsDUEgS7r6+GBqROWHLCFET1OwJMrl/IAZ39GQiQrKK7OCJfsFtoBEC6xK5IiuZHyYjRAY6k1uIg5lXYCMB/7i+YRmR3Cb2q57mu/ZQNrS1R1cTmTgmI0QGqmkVGdbFG22VjjJHQ1Ttvh6+cHW0xfmrpdhzJk/ucIgMwmSEyADlVRpsOMwVV8n0ONkrMK539d5Ia7nwGZkZJiNEBvjj2CVcLalEWzdH3BXqJXc4RHpqNs/bcuwSLheWyxwNUeMxGSEywNqD1b84J/QLgK2CHx8yLV193dAroDWqtELXgkdkDvhtStRImXnFSEjPhyQBE65vUEZkah7tXz2oeu3BLAjBgaxkHpiMEDXS2kPVA1fvCvWCfxuucEmm6f6efmjlYIvM/BLsO5svdzhEjcJkhKgRKqq0WJ9UnYzUTKEkMkUuDrZ4oJcfgL9nfhGZOiYjRI2wNe0S8ooq4OXqgHu6coVLMm2Trg9k/T01B1eKK2SOhujWmIwQNcLqmoGrff1hx4GrZOLC2ikR1s4NFRot4jiQlcwAv1WJbiErvwS7T1cvIsUuGjIXNevgrOFAVjIDTEaIbqFmAakhnTwR4M6Bq2QeHgj3g5OdAumXi5F47qrc4RDdFJMRopuo1GjxQ2J1M/ckrrhKZsTV0Q5jw30BAGsOcEVWMm1MRohuonrgajk8WzlgeDcfucMhMkhNV82vR1VQl1TKHA1Rw5iMEN3E6utTIzlwlcxRr4DW6NLWFeVVWmxM5kBWMl38diVqQNK5K9h96jIADlwl8yRJkq515Lv957D3zGWo1KUyR0VUF5MRonrEHsrC+CX7UDMHYd9ZbslO5umhXu1gayMh/XIxJn9zEIMXbkMsd/UlE8NkhKgWlboUczcc1St7NS6VvyjJLJVUVqFK+/fUXq3g+5lMD5MRoloy8opRe1UGjRDIzCuRJR6i25GRV1ynjO9nMjVMRohqCfF0qVOmkCQEe3KNETI/IZ4ukGqV8f1MpqZJycjixYsREhICR0dHREREYPfu3Tc9ftWqVQgPD4ezszN8fX3x+OOPIz+fu0mSaarSCL0vb4Uk4d1xYfBVOskWE1FT+SqdsHB8D733NN/PZGoMTkZiY2Mxa9YszJs3D8nJyRgyZAhGjx6NrKz6B0Tt2bMHU6dOxRNPPIFjx45h3bp1OHToEJ588snbDp7IGH5IzIYA0C+4DdY8NRB75g5FFGfTkBmL6heI314YAlub6pSkm69S5oiI9BmcjHz88cd44okn8OSTT6Jr165YtGgRAgICsGTJknqP379/P4KDg/H8888jJCQEd9xxB55++mkkJibedvBEza1Ko0Xsoeq1RaYPCkFkBw/+giSL0MXXDff1uL4iK2fTkIkxKBmpqKhAUlISRo4cqVc+cuRIJCQk1HvOoEGDcP78eWzevBlCCFy6dAnr16/HmDFjGnyd8vJyFBQU6N2IWsK2E7nILSyHh4s9RnDFVbIwE/sHAAB+TL6A4vIqmaMh+ptByUheXh40Gg18fPS/pH18fJCTk1PvOYMGDcKqVasQFRUFe3t7tG3bFq1bt8Znn33W4OvExMRAqVTqbgEBAYaESdRkaw5W/2J8pK8/7G05vpssS2R7DwR7OKO4QoNf/roodzhEOk36tpUk/bHZQog6ZTWOHz+O559/Hq+//jqSkpLw+++/IyMjAzNnzmzw+aOjo6FWq3W37OzspoRJZJDzV0uwgyuukgWTJAkTr6/IWrPVAZEpsDXkYE9PTygUijqtILm5uXVaS2rExMRg8ODBeOmllwAAPXv2hIuLC4YMGYK3334bvr6+dc5xcHCAg4ODIaER3bYfDmVDCGBQB496p/cSWYJHIvzx0ZaTOJJ9DakX1Ahrx8GsJD+DWkbs7e0RERGB+Ph4vfL4+HgMGjSo3nNKSkpgY6P/MgqFAkB1iwqRKajSaBGbWP1LsWYvDyJL5NnKAfeGVf8IXHXgnMzREFUzuJtm9uzZ+Oabb7Bs2TKkpaXhxRdfRFZWlq7bJTo6GlOnTtUdP3bsWMTFxWHJkiU4e/Ys9u7di+effx79+/eHn59f89WE6DZsO5GLSwXVA1dHdW8rdzhERvXYgOqEe1PyRRSUVcocDZGB3TQAEBUVhfz8fCxYsAAqlQphYWHYvHkzgoKCAAAqlUpvzZHp06ejsLAQn3/+Of7zn/+gdevWGDZsGN57773mqwXRbfr+wPWBqxEcuEqWr3+IOzp5t8Lp3CJsPHwB0wYFyx0SWTlJmEFfSUFBAZRKJdRqNdzc3OQOhyzMufxi3PXBDgDAzpfuRpAHx4uQ5VuxNwNv/HwcnbxbYcuLdzY4CYHodjT2+s2fgGT1Vl9vFbkr1IuJCFmNcRH+cLJT4HRuEQ5mXJE7HLJyTEbIqpVVavDD9YGrjw0Mkjkaopbj5miHB3tVj9tbdYArspK8mIyQVdt8VIWrJZXwUzpiWBdvucMhalE1CfhvqSrkFZXLHA1ZMyYjZNW+3189tfHR/oFQ2LDPnKxLWDslwgNao1IjdC2ERHJgMkJW6/jFAhzOugZbGwlR/bnlAFmnmmm+qw9kQaM1+fkMZKGYjJDV+v76gk+jwtrC29VR5miI5DE23A9KJzucv1qKXde3QyBqaUxGyCqdyS3EhqTzAIDHBnDgKlkvRzsFHonwBwB8s+csEtLzoFKXyhwVWRsmI2R1Yg9lYcTHu1BepQUAnMsvkjkiInlNvt5Vs/dMPiZ9fQCDF25D7CHOsKGWw2SErIpKXYq5G47ixp7xeRuP8ZcgWTUne4Xefa0AXo1L5eeCWgyTEbIqGXnFqD1ETyMEMvNKZImHyBRk5BXXKePngloSkxGyKiGedVdYVUgSgj2dZYiGyDSEeLqg9sR2fi6oJTEZIatia2MDxQ17cCgkCe+OC4Ov0knGqIjk5at0wsLxPfQSEn4uqCUZvGsvkTn7ITEbGiHQzdcNr93fDcGezvzCJQIQ1S8Qndu64uHFCRAC6BPYRu6QyIqwZYSshkYrdJvizbgjBJEdPJiIEN2gV0AbjOzmAwBYuS9T3mDIqjAZIavxZ9olXLhWitbOdri/p6/c4RCZpGmDggEAcYcvoKCsUt5gyGowGSGrsTIhEwAwsV8gHO0UNz+YyEpFtvdAZx9XlFRosC7xvNzhkJVgMkJW4dSlQiSk58NGAqZEcsVVooZIkoSpg6o/I9/ty4SW+9VQC2AyQlZhxfVWkZHd2qJda44TIbqZh3u3g5ujLTLzS7CT+9VQC2AyQhZPXVKJjYcvAPi7P5yIGuZsb4sJfat3sq5J5ImMickIWbx1SdkordSgs48rBrZ3lzscIrMwJTIIkgTsPHUZZy9z/yYyLiYjZNE0WoFv950DAEwfHAxJqr3OJBHVJ8jDBUM7ewOA7jNEZCxMRsiibT+Ri6wrJVA62eGhXu3kDofIrNR0a65POo+i8ip5gyGLxmSELFrNwk1R/QLq7ExKRDc3pKMn2nu6oKi8CnGHOc2XjIfJCFmsM7mF2H06D5IETBnI6bxEhrKxkTD1+lT4lQmZEILTfMk4mIyQxVqZUN3PPbyrDwLcufsoUVOMj/CHi70C6ZeLsedMntzhkIViMkIWqaCsEhuuNytP53ReoiZzdbTDIxH+AP5exZiouTEZIYu0PvE8Sio06OTdCoM6eMgdDpFZm3o9od96IhdZ+SXyBkMWickIWRyNVugGrk4dxOm8RLerg1cr3BnqBSGA5QkZcodDFojJCFmcdUnZOJdfAldHW4zvw+m8RM3hyTtCAACxh7LxZ1oOVOpSmSMiS8JkhCxK7KEszN1wFABQWFaFn49clDkiIsswpJMnfNwcUFKhwZMrkzB44TbEHsqSOyyyEExGyGKo1KW6RKTGq3Gp/AVH1AxyCsqQW1Cuu68V/HxR82EyQhYjI68YtVdB0AiBzDwOuCO6Xfx8kTE1KRlZvHgxQkJC4OjoiIiICOzevfumx5eXl2PevHkICgqCg4MDOnTogGXLljUpYKKGONezwqpCkhDsyTVGiG5XiKcLbGqNBbcB+PmiZmFwMhIbG4tZs2Zh3rx5SE5OxpAhQzB69GhkZTXcdzhhwgRs3boVS5cuxcmTJ7FmzRp06dLltgInqu231By9+wpJwrvjwuCrdJIpIiLL4at0Qsy4HnoXjafvas/PFzULSRi4vu+AAQPQp08fLFmyRFfWtWtXPPTQQ4iJialz/O+//46JEyfi7NmzcHdv2vbtBQUFUCqVUKvVcHNza9JzkGUrLq/CwJitKCyrwgeP9IR/G2cEezrzi5KomanUpXg1LhXbT+bi3u5t8b8pEXKHRCassddvg1pGKioqkJSUhJEjR+qVjxw5EgkJCfWe89NPP6Fv3754//330a5dO4SGhmLOnDkoLW140FN5eTkKCgr0bkQ3sy4xG4VlVWjv6YLxffwR2cGDiQiREfgqnRB9X3XL9h/Hc7gIGjULg5KRvLw8aDQa+Pj46JX7+PggJyen3nPOnj2LPXv2IDU1FRs3bsSiRYuwfv16PPPMMw2+TkxMDJRKpe4WEBBgSJhkZTRagWV7MwEAM+4IgU3tjm0ialahPq64i4ugUTNq0gDW2itaCiEaXOVSq9VCkiSsWrUK/fv3x3333YePP/4YK1asaLB1JDo6Gmq1WnfLzs5uSphkJeKPX0LWlRK0drbD+D7+codDZBWeHFK9CNoPh7KhLq2UORoydwYlI56enlAoFHVaQXJzc+u0ltTw9fVFu3btoFQqdWVdu3aFEALnz5+v9xwHBwe4ubnp3YgasnTPWQDAYwOC4FTPjBoian53dPREZx9XFFdouPgZ3TaDkhF7e3tEREQgPj5erzw+Ph6DBg2q95zBgwfj4sWLKCoq0pWdOnUKNjY28Pfnr1i6PclZV3Eo8yrsFBKmRgbJHQ6R1ZAkCU9cbx1ZvjcTFVVamSMic2ZwN83s2bPxzTffYNmyZUhLS8OLL76IrKwszJw5E0B1F8vUqVN1x0+aNAkeHh54/PHHcfz4cezatQsvvfQSZsyYAScnDjCk2/O/nekAgAd7tYO3m6PM0RBZlwd7+cHL1QEqdRl+4tYLdBsMTkaioqKwaNEiLFiwAL169cKuXbuwefNmBAVV/ypVqVR6a460atUK8fHxuHbtGvr27YvJkydj7Nix+PTTT5uvFmSV0i8XYcvxSwCAmXe1lzkaIuvjYKvAE9c30PtyZzq0WoNWiiDSMXidETlwnRGqzyvr/0JsYjZGdPPB11P7yh0OkVUqKKvE4JhtKCyvwtdT+2JEt/rHD5J1Mso6I0SmIkddhrjk6gHQM+/qIHM0RNbLzdEOkwdWt4zXdJsSGYrJCJmlZXszUKkR6B/sjoigNnKHQ2TVZgwOhr2tDZLOXcWhzCtyh0NmiMkImR11SSVW7T8HAJh5N8eKEMnN281Rt8bPkh1sHSHDMRkhs/P9gXMortCgs48rhnb2ljscIgLwzzvbQ5KAbSdycSKHW3iQYZiMkFnJyCvCl7uqf3nNvLt9gyv/ElHLCvF0wX1hvgCARfGnkJCeB5W64T3IiG7EZITMRuyhLAz7cCcKSqsAAKUVGpkjIqIb1Qwm//3YJUz6+gAGL9zG1VmpUZiMkFlQqUsxd8NR3DgP/bVNx/jLi8iEeLra693XCuDVuFR+TumWmIyQWcjIK0btBXE0QiAzj9uXE5mKjLziOmX8nFJjMBkhsxDk4VynTCFJCPasW05E8gjxdEHtUVz8nFJjMBkhs3AkW613XyFJeHdcGHyV3N+IyFT4Kp2wcHwPvQvLvDFd+DmlW7KVOwCiW9FqBT7dehpA9eJKI7q1RbCnM7/giExQVL9ADOnkiUe/OoBzV0pwraRS7pDIDLBlhEzen2mXcCKnEC72Cjx/TydEdvBgIkJkwvxaO2Pu6C4AgOV7M6EuZUJCN8dkhEyaEAKfbTsDAJg6KBitne1vcQYRmYJR3dsi1KcVCsursDIhU+5wyMQxGSGTtuPUZRy9oIaTnQJPXt+qnIhMn42NhOeGdQIALN2TgcIyto5Qw5iMkMkSQuCz62NFJg8IhEcrB5kjIiJD3NfDF+29XKAurcR31/eTIqoPkxEyWQnp+TicdQ32tjb4553cEI/I3ChsJDw3rCMA4JvdGSgur5I5IjJVTEbIJAkh8Mn1VpFH+wXA281R5oiIqCnG9vRDkIczrhRXYNUBto5Q/ZiMkElKSM/HwYwrsFfY4Onr+10QkfmxVdjgmaHVrSNf7TrLPaWoXkxGyOQIIfDhlpMAgEkDAuHXmtN4iczZw73bIcDdCXlFFVi5L1PucMgEMRkhk7Pj5GUkZ12Do50N/j2UrSJE5s5OYYNZ94QCAP63Mx0FnFlDtTAZIZNyY6vItMhgeLtyrAiRJXiodzt08HLBtZJKLNuTIXc4ZGKYjJBJ+eNYDo5dLICLvYJjRYgsiMJGwuwRnQFUz6y5Wlwhc0RkSpiMkMnQaAU+jj8FAHjijhC4u3C1VSJLMjqsLbr6uqGovApf7jordzhkQpiMkMn4fn8mTl0qgqujLZ4YwnVFiCyNjY2EOSOrx44s35uBzUcvQqUulTkqMgVMRsgkrD5wDvN/Og4AKCqrwu+pKpkjIiJjGNbFGwHuTiiv0uLfq5IxeOE2xB7KkjsskhmTEZKdSl2KeRtTdfcFgFfjUvmLicgC5RSU4fyVvz/bWsHPOzEZIRNwIqcAolaZRghk5pXIEg8RGU9GXjE/71QHkxGS3cGMK3XKFJKEYE9nGaIhImMK8XSBjaRfZgPw827lmIyQrK4WV+D7/dX9xTXfTwpJwrvjwuCr5MqrRJbGV+mEmHE9oJD+zkg6+7ry827lbOUOgKzb59vPoLCsCt183fD1tAhk5Zci2NOZX0xEFiyqXyDuDPVCwpl8vLz+L6SpCrH/bD4GtveQOzSSCVtGSDbZV0rw7fV9KuaO7oJ2rZ0R2cGDiQiRFfBVOmF8hD8eHRAAAIjZnAattvZoErIWTUpGFi9ejJCQEDg6OiIiIgK7d+9u1Hl79+6Fra0tevXq1ZSXJQvz4ZaTqNQI3NHRE3eGeskdDhHJ4IV7QuFir8CR82r8epRT+q2VwclIbGwsZs2ahXnz5iE5ORlDhgzB6NGjkZV183niarUaU6dOxT333NPkYMlypF5Q48eUiwCqW0WIyDp5uTrotn54/48TKK/SyBwRycHgZOTjjz/GE088gSeffBJdu3bFokWLEBAQgCVLltz0vKeffhqTJk1CZGRkk4MlyyCEwMLfTgAAHuzlh7B2SpkjIiI5PTkkBF6uDsi+Uqob0E7WxaBkpKKiAklJSRg5cqRe+ciRI5GQkNDgecuXL0d6ejrmz5/fqNcpLy9HQUGB3o0sx9a0XOw5kwd7hQ3mjOwsdzhEJDNne1vMHlG9TPxn205DXVopc0TU0gxKRvLy8qDRaODj46NX7uPjg5ycnHrPOX36NObOnYtVq1bB1rZxk3diYmKgVCp1t4CAAEPCJBNWXqXB279WL/v+xJAQBLhzbQEiAv4R4Y9O3q1wraQSn249LXc41MKaNIBVkvRXrBFC1CkDAI1Gg0mTJuHNN99EaGhoo58/OjoaarVad8vOzm5KmGSCViZkIjO/BF6uDnhmaEe5wyEiE2GrsMF/7+8GoPp74kxuocwRUUsyKBnx9PSEQqGo0wqSm5tbp7UEAAoLC5GYmIhnn30Wtra2sLW1xYIFC3DkyBHY2tpi27Zt9b6Og4MD3Nzc9G5k/vKKyvHZ1jMAgJdGdUYrBy5zQ0R/uyvUC8O7eqNKK7DglzQIwam+1sKgZMTe3h4RERGIj4/XK4+Pj8egQYPqHO/m5oajR48iJSVFd5s5cyY6d+6MlJQUDBgw4PaiJ7Py0ZaTKCyvQo92SjzSx1/ucIjIBP13TDfYKSTsOnUZ207kyh0OtRCDf5rOnj0bU6ZMQd++fREZGYmvvvoKWVlZmDlzJoDqLpYLFy7g22+/hY2NDcLCwvTO9/b2hqOjY51ysmw7TuZi7cHq7rbXx3aDTe3NKYiIAAR7umDGHSH4cudZzP/pGOwUEjr5cLl4S2dwMhIVFYX8/HwsWLAAKpUKYWFh2Lx5M4KCggAAKpXqlmuOkHVZe/Ac5sal6u6fvVyEfsHuMkZERKbsuWGdsPpAFs5fLcXUZYdgIwEx43ogql+g3KGRkUjCDDrlCgoKoFQqoVarOX7EzKjUpRgUs01vy3CFJGHP3KH8pUNE9eL3huVo7PWbe9OQUR27qEbtbFcjBDLzSmSJh4hMX0ZeMb83rAyTETKqLccu1SlTSBKCPbm+CBHVL8TTBbWHldkA/N6wYExGyGhSL6ixPuk8gL/faApJwrvjwtjUSkQN8lU6IWZcDyhuWL/Ko5UD3F3sZYyKjIkLPZBRaLUC/92UCq0A7u/pi3ljuiIzrwTBns5MRIjolqL6BeLOUC8cu1CAlzf8hctF5fh611k8O6yT3KGREbBlhIxi7aFspGRfQysHW7x2fzf4Kp0Q2cGDiQgRNZqv0gnDu/lg/tjqlVk/23YG5/KLZY6KjIHJCDW7/KJyvPd79a68s0eEwsfNUeaIiMicPRDuh8EdPVBepcXrPx7jyqwWiMkINbu3f02DurQS3XzdMDUySO5wiMjMSZKEtx4Mg73CBjtPXcbmo/VvzErmi8kINavtJ3KxMfkCbCTg3XE9YKvgW4yIbl97r1b4190dAABv/HwM10oqZI6ImhOvFNRsCssq8erGowCAJ+4IQa+A1vIGREQW5V93d0B7LxdcLizHW7+kyR0ONSMmI9RsFv52Aip1GYI8nDF7RGe5wyEiC+Nop8AHj/SEJAEbDp/H9pPcSM9SMBmhZrH/bD5WHajekyhmXA842StkjoiILFFEkDtmDA4BALwadxSFZZUyR0TNgckI3baMvCK8sDYZAPBo/0AM6uApc0REZMnmjOyMIA9nqNRleO3HVCSk50GlLpU7LLoNTEbotsQeysLQD3fiUkE5AKBz21YyR0REls7JXoGF43oCADYlX8Skrw9g8MJtiD3EHePNFZMRajKVuhRzNxzVK3vr5zT+QiEio6u9T41WAK/GpfL7x0wxGaEm4468RCSXjLy6K7Hy+8d8MRmhJtuQdKFOGXfkJaKWwJ19LQuTEWqS31NV+C01BxK4Iy8Rtbz6dvZ1tFfo3SfzwV17yWC5hWWIjqseK/LvoR3w2MAg7shLRC2uZmffM5eKsODX4zh9qQhz1v+FlY/3g8SkxKywZYQMotUKzFn3F66WVKK7nxteuCeUO/ISkWx8lU4YEuqFJZP7wMHWBrtOXcbKhEy5wyIDMRkhg3y56yx2nboMRzsbLIrqBXtbvoWISH4dvV0xb0xXAEDMbydwIqdA5ojIELySUKMlnbuCD7ecBAAseCAMnXxcZY6IiOhvUwYGYWhnL5RXafHvVYdRVF4ld0jUSExGqFGulVTgudXJ0GgFHuzlh3/09Zc7JCIiPZIk4aMJvdDWzRFnLxdj3sajEKL2AgRkipiM0C0JUT1O5KK6DMEeznjn4R4cHEZEJsndxR6fTeoNhY2EH1MuYu2hbLlDokZgMkI3pVKX4vUfU/Fn2iXYK2zw+aQ+aOXASVhEZLr6BbtjzsjqncPn/3QMu07lcv8aE8erCjUo9lAW5m44qltl9d4wH4S1U8oaExFRYzx9Z3sczMjH9pOXMXXZIQCAjVS9q3hUv0CZo6Pa2DJC9arZd+bG3tZfjqj4y4KIzIKNjYSX7+2sV8b9a0wXkxGq18mcwjr7zmgB7vtARGbjakllnTLuX2OamIxQHUIIbDh8vk45950hInPC/WvMB5MRqmPVgSz8fETFfWeIyKzVt3+NrcIGBaVcf8TUSMIMJmEXFBRAqVRCrVbDzc1N7nAs2q5Tl/H4ikPQaAVeubcLHurtx31niMisqdSlSM8txv/9eQpJ564i0N0ZPz4zGG1c7OUOzeI19vrNlhHSOXWpEM+sOgyNVmBc73aYeVd77jtDRGbPV+mEOzp54uupfeHfxglZV0rwz+8SUVapkTs0uo7JCAEALheW4/Hlh1BYXoX+Ie6IGc+FzYjIsri72GPZ9H5wdbDFocyrmLPuCLRak+8csApNSkYWL16MkJAQODo6IiIiArt3727w2Li4OIwYMQJeXl5wc3NDZGQk/vjjjyYHTM2vrFKDp75NxIVrpQjxdMGXj0XAwVYhd1hERM0u1McV/5sSAVsbCb/8pcIH1/fbInkZnIzExsZi1qxZmDdvHpKTkzFkyBCMHj0aWVlZ9R6/a9cujBgxAps3b0ZSUhKGDh2KsWPHIjk5+baDp9tXpdHiuTXJSMm+htbOdlg2vR/7UYnIog3u6ImF43sCAJbsSMfqA/Vfv6jlGDyAdcCAAejTpw+WLFmiK+vatSseeughxMTENOo5unfvjqioKLz++uuNOp4DWI3j4rUSvBqXih2nLsPe1gbfzeiPAe095A6LiKhFLPrzFBb9eRoKGwkx43rAv40TQjxdOEauGTX2+m3QcvAVFRVISkrC3Llz9cpHjhyJhISERj2HVqtFYWEh3N3dGzymvLwc5eXluvsFBQWGhEmNEHsoC69sOKq7P7GvPxMRIrIqL9zTCReulmJd0nm8vP4vAFwyXi4GddPk5eVBo9HAx8dHr9zHxwc5OTmNeo6PPvoIxcXFmDBhQoPHxMTEQKlU6m4BAQGGhEm3ULPU+41WHcjmEslEZFUkScLzwzvqlXHJeHk0aQBr7VkWQohGzbxYs2YN3njjDcTGxsLb27vB46Kjo6FWq3W37GxuAd2cvtl9ts5S71wimYisUfaVukkHvw9bnkHdNJ6enlAoFHVaQXJzc+u0ltQWGxuLJ554AuvWrcPw4cNveqyDgwMcHBwMCY0aac3BLCzdk1mnnEu9E5E1qlkyvvYMX0nilN+WZFDLiL29PSIiIhAfH69XHh8fj0GDBjV43po1azB9+nSsXr0aY8aMaVqkdNt+OJSN6Ljq7pk7OnpwqXcisnr1LRkPAM+tScHpS4UyRWV9DGoZAYDZs2djypQp6Nu3LyIjI/HVV18hKysLM2fOBFDdxXLhwgV8++23AKoTkalTp+KTTz7BwIEDda0qTk5OUCqVzVgVupkfErPxSlz1AK3pg4Ixf2w35BSUcal3IrJ6Uf0CcWeoFzLzSqB0tsXs2CM4kVOIiV/tx+qnBqJzW1e5Q7R4TdqbZvHixXj//fehUqkQFhaG//u//8Odd94JAJg+fToyMzOxY8cOAMDdd9+NnTt31nmOadOmYcWKFY16PU7tvT3f7z+H135MhRDAtMggvPFAd66uSkTUgKvFFXhs6QEcu1iANs52+P7JAejuxx/PTdHY6zc3yrNwi3ecwfu/V68wyESEiKhx1CWVmLrsAI6cV0PpZIdvZ/RHeEBrucMyO9woz8pdvFaC51Yf1iUizw7tyESEiKiRlM52+O7JAegd2Brq0ko8+vV+bEw+j4T0PE77NQK2jFig1QfO4dWNqbr7Y3q0xReTI2SMiIjIPBWVV+Ff3ydh9+k8XRkXRms8toxYqTO5hXqJCAD8nnqJmTwRURO0crDFOw+H6ZVpBRC94Si/V5sRkxELcuFaKR5fcahOORfwISJquvNX6yYdWgBncotaPhgLxWTEQhw9r8ZDX+ytdzVBLmhGRNR0NQuj1fbJ1tO4VlLR8gFZICYjFmBT8gX848sEXC4sR2cfV8y9t7NuAR8uaEZEdHtqL4xmA8BeYYPEzKt46Iu9OJPLxdFuFwewmrGKKi3e3ZyGFQmZAIA7Q73w+aTecHO0g0pdygXNiIia0Y3fq+rSSjy5MhHnr5ailYMt/i+qF0Z0u/m2KNaI64xYMJW6FIezruLLnWfx13k1gOqpuy+OCIWivrZEIiJqdvlF5fjX94dxMPMKAOCfd7bHlIGByL5aihBPF/4QBJMRixV7KAtzNxzV7brrYGuDzx7tjZHd28oaFxGRNaqo0mLhbyewbG+GXjmn/1bj1F4LdC6/GK/ckIgAQGWVFj38uUwxEZEc7G1t8PrYbogZ10OvXCuAV+NSOf23kZiMmIkzuYWYuuxgnXItwGm7REQyC/KoO2NRIwSOXyyQIRrzY/CuvdSyNFqBZXsy8OGWkyiv0tZ5nNN2iYjkVzP9V1tr4MO8TalwtrdFZAcPeQIzE2wZMWEncwoxbvFevLM5DeVVWgzp5Il593XhtF0iIhNT3/Rfd2c75KjL8OjX+/H6j6koKKuUN0gTxgGsJkSlLkVGXjH8Wjti4+GLWLzjDCo1Aq4Otpg3piui+gVAkiRO2yUiMlE3fj+7OtrhnV/TsOZgFgDA29UB88d2R+9AJTLzS6xixg1n05iZ2rNkagzv6oO3HwpDW6WjLHEREdHt2XM6D//ddBSZ+frj+6xhxg1n05gRlbq03kTkrQe74+upEUxEiIjM2B2dPPH7rDsxY3CwXjk33PsbkxGZXS4sxxs/HauTiABAR29XSBIXMSMiMneOdgoMr2eFVi2Ar3edRZWm7gQFa8LZNDIpKKvE17vOYumeDJRUaOo8zlkyRESWpaEZN8v2ZmLnqct4cUQo7gvzhY0VrqTNlpEWolKXIiE9D6cvFWLxjjO48/3t+GzbGZRUaBDur8RTQ0I4S4aIyILVN+PmoV5+cHexR/rlYjy7Ohn3frILv/x1EReulSAhPc9qunA4gLUFNDQ4taN3K8wZ2RmjuvtwlgwRkZWo/V1fUFaJ5Xsy8c2esygsq9I7VgKwcLz5DnLlbBoTsS89D49+faBO+ev3d8W0QSHc2I6IiAAA6tJKfLbtNL7Zrb/PjQTgt1lD0KWteV3/AM6mkVWVRovfU1WY9PX+ehMRAOjqq2QiQkREOkonOwzr4l2nXAB48PO9eG1TqsUuL88BrM2gZrEye4UN9pzJQ+yhbKjUZQBQ72AlDk4lIqL6NDTItbxKi+/2n8N3+88h3F+Jif0D0S+4DXILyy1i8TQmI7dpRUIG3vzpeJ3xIO4u9pjYLwCTBgRi75k8vBqXCo0QHJxKREQNqhnkeuM1452HuyPQ3QWrDmZhy7EcHDmvxpHzR3XnSADeeTgMkwYEyRf4beKYkSZQl1Ri64lL2JRyAbtO5dV5/I2x3fDogEA42Cp0ZRycSkREjdXQNSO/qBwrEjLx2bYzdc55qLcfovoGon+Iu8kMA2js9ZstI7dQ0wXjbK9A6oUC/HEsB/vS81FVuw3tBp3buuklIkB1tsskhIiIGqOha4ZHKwdEdvCoNxnZlHwRm5Ivwt3FHnd39sI9XXwwJNQTxeVVyMgrNunuHCYjDSipqMIHv5/A8oRz9T7e2ccVgzt6YPneTL0uGo4HISIiY6pvXIkNgDHhvth58jKuFFcg7vAFxB2+oHecBODdcWF4tL/pdecwGbmuoKwSh89dRWLmVSSeu4Kkc1dRqanb+vHvuzvgkQh/tPdqBQDo3NaV40GIiKjF1Deu5N1xYYjqF4hKjRaJmVex/WQu/jiWg3M3bM4nAETHpeLXv3Jwd2cvRHbwQJe2bibRpWPVY0a2HMvBrtOXkZh5FScvFaIx/xNrnhqIyA4eemUcD0JERC3tVteehPQ8TGpgeYkaLvYKhAe0Rp/ANhjT0xddfZt3XCbHjDTC+qTz2HL8ku5+kIcz+ga5o29wG4R4OuPRrw40qguG40GIiKil3era01B3zr+GdsCxiwVIzLyKovIqJKTnIyE9H8GeLs2ejDSWVScjY3r6IsDdGf2C26BPUBt4uzrqPb5wfN1mMCYdRERkDm7WnQMAGq3AqUuFOJx1FYfPXUP/YHfZYm1SN83ixYvxwQcfQKVSoXv37li0aBGGDBnS4PE7d+7E7NmzcezYMfj5+eHll1/GzJkzG/16ck7tZRcMERGZMzmvY0ZbDj42NhazZs3CvHnzkJycjCFDhmD06NHIysqq9/iMjAzcd999GDJkCJKTk/Hqq6/i+eefx4YNGwx96WZXs5PuzXZF9FU6IbKDBxMRIiIyS+ZwHTO4ZWTAgAHo06cPlixZoivr2rUrHnroIcTExNQ5/pVXXsFPP/2EtLQ0XdnMmTNx5MgR7Nu3r1GvaYyWkdhDWYiOOwqtqF6yPWac+e6KSEREZIqM0jJSUVGBpKQkjBw5Uq985MiRSEhIqPecffv21Tl+1KhRSExMRGVlZb3nlJeXo6CgQO/WnFTqUl0iAlQP7nk1LvWmLSRERERkHAYlI3l5edBoNPDx8dEr9/HxQU5OTr3n5OTk1Ht8VVUV8vLqLqUOADExMVAqlbpbQECAIWHeUkZecZ1NiDRCIDOvpP4TiIiIyGgMHjMCAJKkv0CKEKJO2a2Or6+8RnR0NNRqte6WnZ3dlDAbVDPd6UZcOZWIiEgeBiUjnp6eUCgUdVpBcnNz67R+1Gjbtm29x9va2sLDw6PecxwcHODm5qZ3a041050U15MhTtslIiKSj0HrjNjb2yMiIgLx8fF4+OGHdeXx8fF48MEH6z0nMjISP//8s17Zli1b0LdvX9jZ2TUh5OYR1S8Qd4Z6cdouERGRzAzuppk9eza++eYbLFu2DGlpaXjxxReRlZWlWzckOjoaU6dO1R0/c+ZMnDt3DrNnz0ZaWhqWLVuGpUuXYs6cOc1XiyYyh+lOREREls7gFVijoqKQn5+PBQsWQKVSISwsDJs3b0ZQUPUugCqVSm/NkZCQEGzevBkvvvgivvjiC/j5+eHTTz/F+PHjm68WREREZLaseqM8IiIiMh6jrcBKRERE1JyYjBAREZGsmIwQERGRrJiMEBERkayYjBAREZGsmIwQERGRrJiMEBERkayYjBAREZGsmIwQERGRrAxeDl4ONYvEFhQUyBwJERERNVbNdftWi72bRTJSWFgIAAgICJA5EiIiIjJUYWEhlEplg4+bxd40Wq0WFy9ehKurKyRJkjscoysoKEBAQACys7Otbi8ea627tdYbYN2tse7WWm/A+uouhEBhYSH8/PxgY9PwyBCzaBmxsbGBv7+/3GG0ODc3N6t4s9bHWuturfUGWHdrrLu11huwrrrfrEWkBgewEhERkayYjBAREZGsmIyYIAcHB8yfPx8ODg5yh9LirLXu1lpvgHW3xrpba70B6677zZjFAFYiIiKyXGwZISIiIlkxGSEiIiJZMRkhIiIiWTEZISIiIlkxGTEBV69exZQpU6BUKqFUKjFlyhRcu3btluelpaXhgQcegFKphKurKwYOHIisrCzjB9yMmlr3Gk8//TQkScKiRYuMFqOxGFr3yspKvPLKK+jRowdcXFzg5+eHqVOn4uLFiy0XdBMtXrwYISEhcHR0REREBHbv3n3T43fu3ImIiAg4Ojqiffv2+N///tdCkTYvQ+odFxeHESNGwMvLC25uboiMjMQff/zRgtE2L0P/5jX27t0LW1tb9OrVy7gBGpGhdS8vL8e8efMQFBQEBwcHdOjQAcuWLWuhaE2EINnde++9IiwsTCQkJIiEhAQRFhYm7r///puec+bMGeHu7i5eeuklcfjwYZGeni5++eUXcenSpRaKunk0pe41Nm7cKMLDw4Wfn5/4v//7P+MGagSG1v3atWti+PDhIjY2Vpw4cULs27dPDBgwQERERLRg1IZbu3atsLOzE19//bU4fvy4eOGFF4SLi4s4d+5cvcefPXtWODs7ixdeeEEcP35cfP3118LOzk6sX7++hSO/PYbW+4UXXhDvvfeeOHjwoDh16pSIjo4WdnZ24vDhwy0c+e0ztO41rl27Jtq3by9GjhwpwsPDWybYZtaUuj/wwANiwIABIj4+XmRkZIgDBw6IvXv3tmDU8mMyIrPjx48LAGL//v26sn379gkA4sSJEw2eFxUVJR577LGWCNFomlp3IYQ4f/68aNeunUhNTRVBQUFml4zcTt1vdPDgQQHgll/ycurfv7+YOXOmXlmXLl3E3Llz6z3+5ZdfFl26dNEre/rpp8XAgQONFqMxGFrv+nTr1k28+eabzR2a0TW17lFRUeK///2vmD9/vtkmI4bW/bfffhNKpVLk5+e3RHgmi900Mtu3bx+USiUGDBigKxs4cCCUSiUSEhLqPUer1eLXX39FaGgoRo0aBW9vbwwYMACbNm1qoaibR1PqDlTXf8qUKXjppZfQvXv3lgi12TW17rWp1WpIkoTWrVsbIcrbV1FRgaSkJIwcOVKvfOTIkQ3Wc9++fXWOHzVqFBITE1FZWWm0WJtTU+pdm1arRWFhIdzd3Y0RotE0te7Lly9Heno65s+fb+wQjaYpdf/pp5/Qt29fvP/++2jXrh1CQ0MxZ84clJaWtkTIJoPJiMxycnLg7e1dp9zb2xs5OTn1npObm4uioiIsXLgQ9957L7Zs2YKHH34Y48aNw86dO40dcrNpSt0B4L333oOtrS2ef/55Y4ZnVE2t+43Kysowd+5cTJo0yWQ33MrLy4NGo4GPj49euY+PT4P1zMnJqff4qqoq5OXlGS3W5tSUetf20Ucfobi4GBMmTDBGiEbTlLqfPn0ac+fOxapVq2Braxb7t9arKXU/e/Ys9uzZg9TUVGzcuBGLFi3C+vXr8cwzz7REyCaDyYiRvPHGG5Ak6aa3xMREAIAkSXXOF0LUWw5U/2ICgAcffBAvvvgievXqhblz5+L+++83iYF+xqx7UlISPvnkE6xYsaLBY+RkzLrfqLKyEhMnToRWq8XixYubvR7NrXadblXP+o6vr9zUGVrvGmvWrMEbb7yB2NjYepNWc9DYums0GkyaNAlvvvkmQkNDWyo8ozLk767VaiFJElatWoX+/fvjvvvuw8cff4wVK1ZYVeuI+aagJu7ZZ5/FxIkTb3pMcHAw/vrrL1y6dKnOY5cvX66TXdfw9PSEra0tunXrplfetWtX7Nmzp+lBNxNj1n337t3Izc1FYGCgrkyj0eA///kPFi1ahMzMzNuK/XYZs+41KisrMWHCBGRkZGDbtm0m2yoCVL9XFQpFnV+Fubm5Ddazbdu29R5va2sLDw8Po8XanJpS7xqxsbF44oknsG7dOgwfPtyYYRqFoXUvLCxEYmIikpOT8eyzzwKovkALIWBra4stW7Zg2LBhLRL77WrK393X1xft2rWDUqnUlXXt2hVCCJw/fx6dOnUyasymgsmIkXh6esLT0/OWx0VGRkKtVuPgwYPo378/AODAgQNQq9UYNGhQvefY29ujX79+OHnypF75qVOnEBQUdPvB3yZj1n3KlCl1vqBHjRqFKVOm4PHHH7/94G+TMesO/J2InD59Gtu3bzf5i7O9vT0iIiIQHx+Phx9+WFceHx+PBx98sN5zIiMj8fPPP+uVbdmyBX379oWdnZ1R420uTak3UN0iMmPGDKxZswZjxoxpiVCbnaF1d3Nzw9GjR/XKFi9ejG3btmH9+vUICQkxeszNpSl/98GDB2PdunUoKipCq1atAFR/l9vY2MDf379F4jYJco2cpb/de++9omfPnmLfvn1i3759okePHnWmeHbu3FnExcXp7sfFxQk7Ozvx1VdfidOnT4vPPvtMKBQKsXv37pYO/7Y0pe61meNsGiEMr3tlZaV44IEHhL+/v0hJSREqlUp3Ky8vl6MKjVIz1XHp0qXi+PHjYtasWcLFxUVkZmYKIYSYO3eumDJliu74mqm9L774ojh+/LhYunSpWU/tbWy9V69eLWxtbcUXX3yh97e9du2aXFVoMkPrXps5z6YxtO6FhYXC399fPPLII+LYsWNi586dolOnTuLJJ5+UqwqyYDJiAvLz88XkyZOFq6urcHV1FZMnTxZXr17VOwaAWL58uV7Z0qVLRceOHYWjo6MIDw8XmzZtarmgm0lT634jc01GDK17RkaGAFDvbfv27S0evyG++OILERQUJOzt7UWfPn3Ezp07dY9NmzZN3HXXXXrH79ixQ/Tu3VvY29uL4OBgsWTJkhaOuHkYUu+77rqr3r/ttGnTWj7wZmDo3/xG5pyMCGF43dPS0sTw4cOFk5OT8Pf3F7NnzxYlJSUtHLW8JCGujwwjIiIikgFn0xAREZGsmIwQERGRrJiMEBERkayYjBAREZGsmIwQERGRrJiMEBERkayYjBAREZGsmIwQERGRrJiMEBERkayYjBAREZGsmIwQERGRrJiMEBERkaz+H7lH/nB4uPn7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"showing that our piecewise convolution of pdf's works for simple case of adding two normal distros\")\n",
    "sigmaAlt = sigmaE_app\n",
    "print(\"using sigmaB, nu, sigmaE of\",sigmaB,nus[1],sigmaE)\n",
    "nX = 2000\n",
    "halfWidth = 4.*sigmaE\n",
    "x = [-halfWidth + 2.*halfWidth*(i+0.5)/nX for i in range(nX)]\n",
    "n_cdf = [norm.cdf(x[i],0,sigmaB) for i in range(nX)]\n",
    "normB =   [norm.pdf(x[i],0,sigmaB) for i in range(nX)]\n",
    "normAlt = [norm.pdf(x[i],0,sigmaAlt) for i in range(nX)]\n",
    "t_pdf = [t.pdf(x[i],nu,0,sigmaE) for i in range(nX)]\n",
    "convo = [0.]*nX\n",
    "dw = 1./nX\n",
    "fudge = (2*3.1415926/3) **0.5 #2**0.5  #not sure why this fudge factor works\n",
    "for i in range(nX):\n",
    "    if i%int(nX/10) == 0:\n",
    "        print(\"working on i=\",i,\"out of\",nX)\n",
    "    for j in range(nX):\n",
    "        thisX = x[i]+x[j]\n",
    "        if thisX >= x[0] and thisX <= x[-1]:\n",
    "            thisI_0 = int( i+0.5 - (nX-1)/2. + (j - (nX-1)/2.) + (nX-1)/2.)\n",
    "            thisI_1 = int( i+0.5 - (nX-1)/2. + (j +0.5- (nX-1)/2.) + (nX-1)/2.)\n",
    "            #xDist = [(x[i] - thisX)**2 for i in range(nX) ]\n",
    "            #thisI = xDist.index(np.min(xDist) )\n",
    "            convo[thisI_0] +=  fudge*0.5*dw * normB[i] * normAlt[j]\n",
    "            convo[thisI_1] +=  fudge*0.5*dw * normB[i] * normAlt[j]\n",
    "            #convo[thisI_0] +=  fudge*0.5*dw * normB[i] * t_pdf[j]\n",
    "            #convo[thisI_1] +=  fudge*0.5*dw * normB[i] * t_pdf[j]\n",
    "fudgeScale = np.sum(convo) / nX\n",
    "#convo = [convo[i]/fudgeScale for i in range(nX)]\n",
    "truePDF = [norm.pdf(x[i],0, (sigmaAlt*sigmaAlt +sigmaB*sigmaB)**0.5) for i in range(nX)]\n",
    "plt.scatter([x[i] for i in range(0,nX,40)],[convo[i] for i in range(0,nX,40)],label=\"convoluted pdf\",marker=\".\")\n",
    "plt.plot(x,truePDF, label=\"true 2-normal pdf\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "c35bbed9-f560-454b-8f05-9da945b1e792",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "And is our CDF correct for the convolution?\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"And is our CDF correct for the convolution?\")\n",
    "convoCDF = [0. for i in range(nX)]\n",
    "for i in range(nX):\n",
    "    convoCDF[i] = [(np.sum(convo[0:max(0,i-1)])+0.5*x[i] )/float(nX)]\n",
    "\n",
    "plt.scatter([x[i] for i in range(0,nX,40)],[convoCDF[i]/np.max(convoCDF) for i in range(0,nX,40)],label=\"convo CDF\",marker=\"o\")\n",
    "\n",
    "trueCDF = [norm.cdf(x[i],0, (sigmaAlt*sigmaAlt +sigmaB*sigmaB)**0.5) for i in range(nX)]\n",
    "plt.plot(x, trueCDF,label=\"true CDF\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "83880552-5df3-4ef1-8c4a-9b9d95f05428",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "bf480bbc-e596-4f66-b476-f12f8207da5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now build a table that convolutes t-distro with normal distro for logit(vote) = mean + N(sigmaB) + t(nu,sigmaE)\n",
      "using sigmaB, nu, sigmaE of 0.117 2.896 0.18 from Kenny-Imai 2023\n",
      "working on i= 0 out of 2000\n",
      "working on i= 200 out of 2000\n",
      "working on i= 400 out of 2000\n",
      "working on i= 600 out of 2000\n",
      "working on i= 800 out of 2000\n",
      "working on i= 1000 out of 2000\n",
      "working on i= 1200 out of 2000\n",
      "working on i= 1400 out of 2000\n",
      "working on i= 1600 out of 2000\n",
      "working on i= 1800 out of 2000\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Now build a table that convolutes t-distro with normal distro for logit(vote) = mean + N(sigmaB) + t(nu,sigmaE)\")\n",
    "sigmaAlt = sigmaE_app\n",
    "print(\"using sigmaB, nu, sigmaE of\",sigmaB,nus[1],sigmaE,\"from Kenny-Imai 2023\")\n",
    "nX = 2000\n",
    "halfWidth = 4.*sigmaE\n",
    "x = [-halfWidth + 2.*halfWidth*(i+0.5)/nX for i in range(nX)]\n",
    "n_cdf = [norm.cdf(x[i],0,sigmaB) for i in range(nX)]\n",
    "n_pdf = [norm.cdf(x[i],0,sigmaB) for i in range(nX)]\n",
    "t_pdf = [norm.cdf(x[i],0,sigmaAlt) for i in range(nX)]  #uncomment, replace with below\n",
    "normB =   [norm.pdf(x[i],0,sigmaB) for i in range(nX)]\n",
    "normAlt = [norm.pdf(x[i],0,sigmaAlt) for i in range(nX)]\n",
    "t_pdf = [t.pdf(x[i],nus[1],0,sigmaE) for i in range(nX)]\n",
    "convo = [0.]*nX\n",
    "dw = 1./nX\n",
    "fudge = (2*3.1415926/3) **0.5 #2**0.5  #not sure why this fudge factor works\n",
    "for i in range(nX):\n",
    "    if i%int(nX/10) == 0:\n",
    "        print(\"working on i=\",i,\"out of\",nX)\n",
    "    for j in range(nX):\n",
    "        thisX = x[i]+x[j]\n",
    "        if thisX >= x[0] and thisX <= x[-1]:\n",
    "            thisI_0 = int( i+0.5 - (nX-1)/2. + (j - (nX-1)/2.) + (nX-1)/2.)\n",
    "            thisI_1 = int( i+0.5 - (nX-1)/2. + (j +0.5- (nX-1)/2.) + (nX-1)/2.)\n",
    "            #xDist = [(x[i] - thisX)**2 for i in range(nX) ]\n",
    "            #thisI = xDist.index(np.min(xDist) )\n",
    "            #convo[thisI_0] +=  fudge*0.5*dw * normB[i] * normAlt[j]\n",
    "            #convo[thisI_1] +=  fudge*0.5*dw * normB[i] * normAlt[j]\n",
    "            convo[thisI_0] +=  fudge*0.5*dw * normB[i] * t_pdf[j]\n",
    "            convo[thisI_1] +=  fudge*0.5*dw * normB[i] * t_pdf[j]\n",
    "sigmaApp = (sigmaAlt*sigmaAlt +sigmaB*sigmaB)**0.5\n",
    "truePDF = [norm.pdf(x[i],0,sigmaApp)  for i in range(nX) ]\n",
    "plt.scatter(x,convo,label=\"convoluted pdf,nu,sig=\"+str(r3(nus[1]))+\",\"+str(r3(sigmaE)),marker=\".\")\n",
    "plt.plot(x,truePDF, label=\"normal approx, sd =\"+str(round(sigmaApp,3)) )\n",
    "plt.legend()\n",
    "plt.show()\n",
    "                    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "21c84130-3d28-4647-a5cc-300be905868b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here, we compare normal + t distribution to a t distribution with higher nu\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Here, we compare normal + t distribution to a t distribution with higher nu\")\n",
    "appSIGMA = (sigmaAlt*sigmaAlt +sigmaB*sigmaB)**0.5\n",
    "plt.scatter([x[i] for i in range(0,nX,20)],[convo[i] for i in range(0,nX,20)],marker=\"o\",label=\"convol\")\n",
    "guessedNus = [3,4,5, 10]   #tomorrow, let's try fitting GA-12 results with nu = 4, sigmaTotal = 0.226\n",
    "guessedScales = [1.13, 1.12, 1.1, 1.05]\n",
    "for jj, nu in enumerate(guessedNus):\n",
    "    appS = appSIGMA / guessedScales[jj]\n",
    "    truePDF = [t.pdf(xx,nu,0,appS) for xx in x]\n",
    "\n",
    "    plt.plot(x,truePDF, label=\"approx pdf,nu =\"+str(nu)+\" appS = \"+str(r3(appS)))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "4c71d473-acb1-4b5a-b304-e14898a3401f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "convoCDF = [0. for i in range(nX)]\n",
    "for i in range(nX):\n",
    "    convoCDF[i] = [(np.sum(convo[0:max(0,i-1)])+0.5*x[i] )/float(nX)]\n",
    "convoCDF = [convoCDF[i] / np.max(convoCDF) for i in range(nX) ]  #idiot-proof normalization\n",
    "plt.scatter([x[i] for i in range(0,nX,40)],[convoCDF[i] for i in range(0,nX,40)],label=\"convo CDF\",marker=\"o\")\n",
    "plt.plot(x,[t.cdf(xx,5,0,0.22) for xx in x],label=\"nu5 appS0.22\")\n",
    "plt.plot(x,[t.cdf(xx,1.5,0,0.18) for xx in x],label=\"nu1.5 appS0.18\")\n",
    "plt.plot(x,[norm.cdf(xx,0.,0.24) for xx in x],label=\"logit norm sig0.024\")\n",
    "plt.scatter([math.log(0.561/(1-0.561)),math.log(0.511/(1.-0.511))],[0.83,0.59],marker=\"x\",label=\"GA-12\")\n",
    "plt.axhline(0.5,ls=\"--\")\n",
    "plt.axvline(0.,ls=\"--\")\n",
    "plt.xlabel(\"logit(vote share)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "d05973d7-61af-4ff5-b90f-bc158706fcaa",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5360274546127911 [0.72911085] 1200\n"
     ]
    }
   ],
   "source": [
    "print(voteFromLogit[i], convoCDF[i], i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "e485668f-aa41-4442-8754-cae852caddec",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seat expectation vs. vote share for above convoluted CDF\n",
      "vote, seat exp\n",
      "0.51017 0.56723\n",
      "0.51035 0.56846\n",
      "0.51053 0.56968\n",
      "0.51071 0.57089\n",
      "0.51089 0.57211\n",
      "0.51107 0.57333\n",
      "0.51125 0.57455\n",
      "0.51143 0.57576\n",
      "0.51161 0.57698\n",
      "0.51179 0.57819\n",
      "0.51197 0.57941\n",
      "0.5601 0.84209\n",
      "0.56028 0.84277\n",
      "0.56045 0.84344\n",
      "0.56063 0.84412\n",
      "0.56081 0.84479\n",
      "0.56098 0.84546\n",
      "0.56116 0.84612\n",
      "0.56134 0.84679\n",
      "0.56152 0.84745\n",
      "0.56169 0.84811\n",
      "0.56187 0.84877\n"
     ]
    }
   ],
   "source": [
    "print(\"seat expectation vs. vote share for above convoluted CDF\")\n",
    "print(\"vote, seat exp\")\n",
    "voteFromLogit = [math.exp(L)/(1+math.exp(L)) for L in x]\n",
    "for i in range(nX):\n",
    "    if abs(voteFromLogit[i] - 0.511) < 0.001:\n",
    "        print(round(voteFromLogit[i],5),round(convoCDF[i][0],5))\n",
    "    if abs(voteFromLogit[i] - 0.561) < 0.001:\n",
    "        print(round(voteFromLogit[i],5),round(convoCDF[i][0],5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "7704531b-9b8e-4726-8857-6bcd1bc9add8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now showing seat expectations on a linear vote scale\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Now showing seat expectations on a linear vote scale\")\n",
    "KennyV, KennyS = [0.561, 0.511], [0.83, 0.59]\n",
    "nVotes = 31\n",
    "votes = [0.5 + 0.01*i for i in range(31)]\n",
    "voteLogits = [math.log(v/(1-v)) for v in votes]\n",
    "nu, nuSigma = 1.5, 0.18  #7, 0.24\n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "#nuSeats = [math.exp(nSL)/(1.+math.exp(nSL)) for nSL in nuSeatLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "plt.scatter(KennyV,KennyS,label=\"Kenny GA-12\",marker=\"x\")\n",
    "plt.plot(votes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "nu, nuSigma = 3, 0.22  #7, 0.24\n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "#nuSeats = [math.exp(nSL)/(1.+math.exp(nSL)) for nSL in nuSeatLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "plt.plot(votes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "mySigma = 0.065\n",
    "normSeats = [norm.cdf(v,0.5,mySigma) for v in votes]\n",
    "plt.plot(votes,normSeats,label=\"Norm=\"+str(mySigma))\n",
    "mySigma = 0.061\n",
    "normSeats = [norm.cdf(v,0.5,mySigma) for v in votes]\n",
    "plt.plot(votes,normSeats,label=\"Norm=\"+str(mySigma),ls=\"--\")\n",
    "convoCleaned = [convoCDF[i][0] for i in range(nX)]\n",
    "plt.plot(voteFromLogit[int(0.5*nX):-1],convoCleaned[int(0.5*nX):-1],label=\"convoKenny\")\n",
    "plt.xlabel(\"fraction GOP votes\")\n",
    "plt.ylabel(\"GOP seat expectation\")\n",
    "plt.axhline(0.5,ls=\"--\")\n",
    "plt.axvline(0.5,ls=\"--\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78576099-4f64-4323-b92d-095481941611",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"Overall result -- the GA-12 example shows a greater chance for minority candidate in deep red/blue districts than my gut expectation\")\n",
    "print(\"We could use the nu=1.5, nuSigma = 0.18 approximation\")\n",
    "print(\"Or waffle a bit and use nu=3, nuSigma=0.22\")\n",
    "print(\"For either of these, convert votes to logit scale, seat expectation is direct outcome from nu cdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "18a892ea-c969-4850-8130-085d210352a7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now read in the CoryVotesSeats table that approximates KennyImai r model for votes to seats\n",
      "Here is the votes --> seats on linear scale for the KennyImai V-to-S model\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Now read in the CoryVotesSeats table that approximates KennyImai r model for votes to seats\")\n",
    "infile = \"./CoryVotesSeats.csv\"\n",
    "inDF = pd.read_csv(infile)\n",
    "tableVotes = inDF['voteFrac']\n",
    "tableSeats = inDF['seatFrac']\n",
    "print(\"Here is the votes --> seats on linear scale for the KennyImai V-to-S model\")\n",
    "plt.scatter(tableVotes, tableSeats)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a1fb16ea-caa1-41f3-891e-cb08959f6f37",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "voteLogits = [math.log(v/(1-v)) for v in tableVotes]\n",
    "\n",
    "nu, nuSigma = 5, 0.2335 #7, 0.24\n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "#plt.plot(tableVotes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "#plt.scatter(tableVotes, tableSeats,label=\"Cory\")\n",
    "offSet = [nuSeats[i] - tableSeats[i] for i in range(len(tableSeats)) ]\n",
    "plt.scatter(tableVotes,offSet, label=\"offSet\"+str(r3(np.sum(offSet))) )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a033bbbb-56be-45f0-8d4b-dcfaf56af594",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "voteLogits = [math.log(v/(1-v)) for v in tableVotes]\n",
    "\n",
    "nu, nuSigma = 4.2, 0.2251   \n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "#plt.plot(tableVotes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "#plt.scatter(tableVotes, tableSeats,label=\"Cory\")\n",
    "tRows = len(tableVotes)\n",
    "offSet = [nuSeats[i] - tableSeats[i] for i in range(tRows) ]\n",
    "rmse = (np.sum([(nuSeats[i] - tableSeats[i])**2 for i in range(tRows)]) / tRows )**0.5\n",
    "plt.scatter(tableVotes,offSet, label=\"offSet\"+str(r3(np.sum(offSet)))+\" rmse\"+str(r5(rmse)) )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "d2affa30-1e0d-4f0c-8432-ce41127ab210",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "voteLogits = [math.log(v/(1-v)) for v in tableVotes]\n",
    "\n",
    "nu, nuSigma = 4, 0.2233  #7, 0.24\n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "#plt.plot(tableVotes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "#plt.scatter(tableVotes, tableSeats,label=\"Cory\")\n",
    "tRows = len(tableVotes)\n",
    "offSet = [nuSeats[i] - tableSeats[i] for i in range(tRows) ]\n",
    "rmse = (np.sum([(nuSeats[i] - tableSeats[i])**2 for i in range(tRows)]) / tRows )**0.5\n",
    "plt.scatter(tableVotes,offSet, label=\"offSet\"+str(r3(np.sum(offSet)))+\" rmse\"+str(r5(rmse)) )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "d0a3005c-fd9f-4a79-9728-72e15d3f2640",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkEAAAGdCAYAAAAVEKdkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABAsElEQVR4nO3de3yT9d3/8XdaeoBKI+e0glARga5s0CJQUHHKoTpBvFVAb+rclAmeqNWf4DwAMmF1Tp1D8MRhGw553EMUbrGjTEWBKnJSS6tOLHJK5WiKSqG01++P3slIk7RJmzSn1/PxyONBrnxz5cqVi+aT7/fz/XxNhmEYAgAAiDIxwT4AAACAYCAIAgAAUYkgCAAARCWCIAAAEJUIggAAQFQiCAIAAFGJIAgAAEQlgiAAABCVWgX7AEJVbW2tDh48qLZt28pkMgX7cAAAgBcMw9CJEyeUmpqqmJiG+3oIgjw4ePCgunXrFuzDAAAATbBv3z517dq1wTYEQR60bdtWUt1JTE5ODvLRAAAAb1RWVqpbt26O7/GGEAR5YB8CS05OJggCACDMeJPKQmI0AACISgRBAAAgKhEEAQCAqEROEAA0oKamRtXV1cE+DABniYuLU2xsbLP3QxAEAB58//332r9/vwzDCPahADiLyWRS165ddc455zRrPwRBAOBGTU2N9u/frzZt2qhTp04UTQVChGEYOnz4sPbv369evXo1q0eIIAgA3KiurpZhGOrUqZNat24d7MMBcJZOnTppz549qq6ublYQRGI0ADSAHiAg9Pjr/yU9QWhUTa2hLeXHdOhElTq3TdSgtPaKjeGLAQAQ3giC0KDCEqtmrymV1Vbl2JZiTtTMMenKyUgJ4pEBANA8DIfBo8ISq6Yu2+4UAElSha1KU5dtV2GJNUhHBqA5Nm3apH79+ikuLk7jxo3zuA2IdARBcKum1tDsNaVyNzHYvm32mlLV1BqO9sW7j+rNnQdUvPuoYzuA0JOfn6/+/furvLxcS5cu9bht5cqVGjx4sMxms9q2bauf/OQnuv/++316LZPJpDfeeMOrtitXrlR6eroSEhKUnp6uVatWNfqczz77TMOHD1fr1q113nnn6fHHH3cpabBhwwZlZWUpMTFRF1xwgV544QWnx19++WVdeumlateundq1a6cRI0Zoy5YtXr/HULBgwQKlpaUpMTFRWVlZ+uCDDxp9TmPnRWr8M3n//fc1ZswYpaamuv2sq6urNX36dPXr109JSUlKTU3VLbfcooMHDzq1u/zyy2UymZxuEydO9P1E+IggCG5tKT/m0gN0NkOS1ValLeXHVFhi1SUF7+imlz/UtNd26qaXP9QlBe/QUwQoNH8g7N69W1dccYW6du2qc8891+229evXa+LEibrhhhu0ZcsWbdu2TU888YROnz4dkGMqLi7WhAkTlJubq08++US5ubkaP368PvroI4/Pqays1MiRI5WamqqPP/5Yf/7zn/XUU0/p6aefdrQpLy/X1VdfrUsvvVQ7duzQb3/7W917771auXKlo817772nm266Se+++66Ki4t1/vnna9SoUTpw4IDXx19TU6Pa2tqmvflmWrFihfLy8vTwww9rx44duvTSS3XVVVdp7969Hp/jzXnx5jP54Ycf9LOf/Uzz5893+zo//vijtm/frkcffVTbt2/X66+/ri+//FJjx451aTt58mRZrVbH7cUXX2zGWfGSAbdsNpshybDZbME+lKB4Y8d+o/v0/230Nnt1idHDzfYe/3d7+7ODjn2eqak1Nn91xHhjx35j81dHjDM1tUF8h0DDTp48aZSWlhonT55s8j7e/uygMWTueqf/G0Pmrnf6f+FvVVVVxj333GN06tTJSEhIMIYNG2Zs2bLFMAzDKC8vN1T3G8ZxW7Jkidtt06ZNMy6//PJGX2/16tVGZmamkZCQYKSlpRmzZs0yqqurDcMwjO7duzvtt3v37h73M378eCMnJ8dp2+jRo42JEyd6fM6CBQsMs9lsVFVVObbNmzfPSE1NNWpr6/6+PPjgg0afPn2cnnfHHXcYQ4YM8bjfM2fOGG3btjX+8pe/eGyzZMkSw2w2G2vWrDH69u1rxMbGGl9//bXRvXt3Y86cOUZubq6RlJRknH/++cYbb7xhHDp0yBg7dqyRlJRkZGRkGB9//LFjX3v27DGuueYa49xzzzXatGljpKenG2+99Zbj8V27dhlXXXWVkZSUZHTu3NmYNGmScfjwYcfjgwYNMqZMmeJ0fH369DFmzJjh8fi9OS++fiaSjFWrVnl8TbstW7YYkoxvvvnGsW348OHGtGnTGn2uXUP/P335/qYnCG51bpvoVbs3dh70asiM3iJEm2Dl1D344INauXKl/vKXv2j79u268MILNXr0aB07dkzdunWT1WpVcnKynn32WVmtVt14440u2yZMmCCLxaJdu3appKTE42v985//1KRJk3TvvfeqtLRUL774opYuXaonnnhCkvTxxx9LkpYsWSKr1eq4705xcbFGjRrltG306NHavHlzg88ZPny4EhISnJ5z8OBB7dmzp8H9bt261eNyKD/++KOqq6vVvn17j69tbzdv3jy98sor2rVrlzp37ixJeuaZZzRs2DDt2LFDv/jFL5Sbm6tbbrlFkyZNcnwmt9xyi2PY7q677tKpU6f0/vvv67PPPlNBQYGjErLVatXw4cPVv39/bd26VYWFhfr22281fvx4SdLp06e1bds2l/c4atSoRs9dY+elKZ+JN2w2m0wmk6MX0u7VV19Vx44d9ZOf/EQPPPCATpw40azX8QZBENwalNZeKeZEeZoIb5LUPilOx37w3DVuHzKb/85XJFgjqviaU+cvP/zwgxYuXKg//OEPuuqqq5Senq6XX35ZrVu31qJFixQbGyuLxSKTySSz2SyLxaKkpCSXba1bt9Y999yjiy++WP369VOPHj00ceJELV68WKdOnXK83hNPPKEZM2bol7/8pS644AKNHDlSc+bMcQxjdOrUSZJ07rnnymKxOO67U1FRoS5dujht69KliyoqKnx+jv2xhtqcOXNGR44ccbvfGTNm6LzzztOIESM8vrZUl++yYMECDR06VL1791ZSUpIk6eqrr9Ydd9yhXr166bHHHtOJEyd08cUX68Ybb9RFF12k6dOnq6ysTN9++60kae/evRo2bJj69eunCy64QNdcc40uu+wySdLChQuVmZmpuXPnqk+fPhowYIAWL16sd999V19++aWOHDmimpoav527s89LUz6TxlRVVWnGjBm6+eablZyc7Nj+3//931q+fLnee+89Pfroo1q5cqX+67/+q8mv4y2CoCjnKV8hNsakmWPSJcklELLfv67/eV69xpJN5S3+ZQAEky85df60e/duVVdXa9iwYY5tcXFxGjRokMrKynzaV1JSkt566y199dVXeuSRR3TOOefo/vvv16BBg/Tjjz9KkrZt26bHH39c55xzjuNmz+uwt6lv7969Tu3nzp3reKx+ATzDMBotiufuOfW3e9PG7sknn9Ty5cv1+uuvKzGx4R7x+Ph4/fSnP3XZfvY2exDRr18/l22HDh2SJN1777363e9+p2HDhmnmzJn69NNPHW23bdumd9991+mc9enTR1Ld593QewzUuWtqocLq6mpNnDhRtbW1WrBggdNjkydP1ogRI5SRkaGJEyfqH//4h9avX6/t27c36bW8RZ2gKNZYDaCcjBQtnJTp0sbyf23MreO1aNOeRl/nu5OeV+A++8sgu2eH5rwdIGQcOuE5AGpKO295+nJvzhdXz5491bNnT91+++16+OGHddFFF2nFihX61a9+pdraWs2ePdvtL3ZPAURqaqp27tzpuG8fcrJYLC49DIcOHXLpiTibp+dI/wk0PLVp1aqVOnRw/pvz1FNPae7cuVq/fr3b4Ka+1q1buz2vcXFxjn/bH3e3zZ5Iffvtt2v06NF66623tG7dOs2bN09//OMfdc8996i2tlZjxoxRQUGBy+ukpKQ4VlP317k7+7w05TPxpLq6WuPHj1d5ebneeecdp14gdzIzMxUXF6d///vfyszM9Pn1vEVPUJTyNl8hJyNFG6dfoeWTh+hPE/tr+eQh2jj9CuVkpHg1ZHZu6zgPjzrz95cBEEze5tR5285bF154oeLj47Vx40bHturqam3dulV9+/Zt9v579OihNm3a6IcffpBU90X1xRdf6MILL3S5xcTUfb3ExcWppqbGsY9WrVo5tbMHQdnZ2SoqKnJ6vXXr1mno0KEejyc7O1vvv/++04y1devWKTU1VT169GhwvwMHDnQKTP7whz9ozpw5Kiws1MCBA5twdpqnW7dumjJlil5//XXdf//9evnllyXVneNdu3apR48eLuc4KSlJ8fHxysrKcnmPRUVFjZ67xs5LUz4Td+wB0L///W+tX7/eJfh0Z9euXaqurlZKSmCL8hIERSFf8xViY0zK7tlB1/Y/T9k9OziWzPBmyOxXw3p4dUz+/jIAgsmbHwgp5rolaPwpKSlJU6dO1f/7f/9PhYWFKi0t1eTJk/Xjjz/qtttu82lfs2bN0oMPPqj33ntP5eXl2rFjh37961+rurpaI0eOlCQ99thj+utf/6pZs2Zp165dKisr04oVK/TII4849tOjRw/961//UkVFhY4fP+7x9aZNm6Z169apoKBAn3/+uQoKCrR+/Xrl5eU52syfP19XXnml4/7NN9+shIQE3XrrrSopKdGqVas0d+5c5efnO3pbpkyZom+++Ub5+fkqKyvT4sWLtWjRIj3wwAOO/Tz55JN65JFHtHjxYvXo0UMVFRWqqKjQ999/79M5a6q8vDz985//VHl5ubZv36533nnHEbTeddddOnbsmG666SZt2bJFX3/9tdatW6df//rXjuAyPz9fr7zyihYvXqyysjLdd9992rt3r6ZMmeJ4jYceeki33HKL474358Wbz+T777/Xzp07Hb175eXl2rlzp2N6/pkzZ3TDDTdo69atevXVV1VTU+M4v/bgdffu3Xr88ce1detW7dmzR2vXrtWNN96oAQMGOA3tBkKLBEG+FnHyRwGnefPm6eKLL1bbtm3VuXNnjRs3Tl988YVf31e48me+gn3IzGJ2DmIs5kQtnJSpu6/oFZQvAyCYvPmBMHNMekDW4Pv973+v66+/Xrm5ucrMzNRXX32lf/7zn2rXrp1P+xk+fLi+/vpr3XLLLerTp4+uuuoqVVRUaN26derdu7ekuplC//u//6uioiJdfPHFGjJkiJ5++ml1797dsZ8//vGPKioqUrdu3TRgwACPrzd06FC99tprWrJkiX76059q6dKlWrFihQYPHuxoc+TIEac8GLPZrKKiIu3fv18DBw7UnXfeqfz8fOXn5zvapKWlae3atXrvvffUv39/zZkzR88995yuv/56R5sFCxbo9OnTuuGGG5SSkuK4PfXUUz6ds6aqqanRXXfdpb59+yonJ0e9e/d25MykpqZq06ZNqqmp0ejRo5WRkaFp06bJbDY7etsmTJigZ599Vo8//rj69++v999/X2vXrnX6HKxWq1PdIG/OizefydatWzVgwADHZ5ufn68BAwbosccekyTt379fq1ev1v79+9W/f3+n82ufZRYfH69//etfGj16tHr37q17771Xo0aN0vr165u1Qrw3TIZhBDQjdcWKFcrNzdWCBQs0bNgwvfjii3rllVdUWlqq888/36V9eXm5MjIyNHnyZN1xxx3atGmT7rzzTi1fvtzx4RQXF+vSSy/VnDlzdN1112nVqlV67LHHtHHjRseHk5OTo4kTJ+riiy/WmTNn9PDDD+uzzz5TaWmpI4O/IZWVlTKbzbLZbI2OXYabN3ce0LTXdjba7k8T++taL5OfG1pk1T70Jsmp98n+53/hpEzWIUPIqaqqUnl5ueMHXFOw9h4QGA39//Tl+zvgQdDgwYOVmZmphQsXOrb17dtX48aN07x581zaT58+XatXr3aayTBlyhR98sknKi4ullQX9VZWVurtt992tMnJyVG7du20fPlyt8dx+PBhde7cWRs2bHBMPWxIJAdBxbuP6qaXP2y03fLJQ/yWrMyXAcKNP4IgqeEfCACaxl9BUEBnh9mLOM2YMcNpe0NFnDwVZ1q0aJGqq6sVFxen4uJi3XfffS5tnn32WY/HYrPZJMlj8atTp0451b+orKz0uK9wZ89XqLBVuc0LMqluOMufQ1Q5GSkamW7hywBRx55TByD0BDQnqClFnAJRwMkwDOXn5+uSSy5RRkaG2zbz5s2T2Wx23Lp16+bVewxHwcpX8JRgDQBAMLRIYrSvNSv8XcDp7rvv1qeffupxqEyqy5y32WyO2759+zy2jQSNJTQzRAUAiHQBHQ7r2LGjz0Wc/F3A6Z577tHq1av1/vvvq2vXrh6PNSEhwWn9mWjAEBXQuACnTQJoAn/9vwxoT1BTijj5q4CTYRi6++679frrr+udd95RWlqaP95SxGGICnDPPjX37EJ8AEKD/f9lc6fQB3zZjPz8fOXm5mrgwIHKzs7WSy+95FTE6aGHHtKBAwf017/+VVLdTLD58+crPz9fkydPVnFxsRYtWuQ0lDVt2jRddtllKigo0LXXXqs333xT69evd6qSetddd+nvf/+73nzzTbVt29bRc2Q2m9W6detAv20AYa5Vq1Zq06aNDh8+rLi4OEdNFgDBVVtbq8OHD6tNmzZq1ap5YUzAp8hLdYWonnzySVmtVmVkZOiZZ55xTFO/9dZbtWfPHr333nuO9hs2bNB9992nXbt2KTU1VdOnT3eqfClJ//jHP/TII4/o66+/Vs+ePfXEE084rV/jKT9oyZIluvXWWxs95kieIg/AO6dPn1Z5ebljjScAoSEmJkZpaWmKj493eSyk6gSFK4IgAFLdr06GxIDQEh8f77F3NmTqBAFAuIuJiWlWsUQAoYtBbgAAEJUIggAAQFQiCAIAAFGJIAgAAEQlgiAAABCVCIIAAEBUIggCAABRiSAIAABEJYIgAAAQlQiCAABAVGLZDISUmlpDW8qP6dCJKnVum6hBae0VG+N+MVwAAJqDIAgho7DEqtlrSmW1VTm2pZgTNXNMunIyUoJ4ZACASMRwGEJCYYlVU5dtdwqAJKnCVqWpy7arsMQapCMDAEQqgiAEXU2todlrSmW4ecy+bfaaUtXUumsBAEDTEAQh6LaUH3PpATqbIclqq9KW8mMtd1AAgIhHEISgO3TCcwDUlHYAAHiDIAhB17ltol/bAQDgDYIgBN2gtPZKMSfK00R4k+pmiQ1Ka9+ShwUAiHAEQQi62BiTZo5JlySXQMh+f+aYdOoFAQD8iiAIISEnI0ULJ2XKYnYe8rKYE7VwUiZ1ggAAfkexRISMnIwUjUy3UDEaANAiCIIQUmJjTMru2SHYhwEAiAIMhwEAgKhEEAQAAKISQRAAAIhKBEEAACAqEQQBAICoxOywCFZTazDdHAAADwiCIlRhiVWz15Q6rc6eYk7UzDHpFB4EAEAMh0WkwhKrpi7b7hQASVKFrUpTl21XYYk1SEcGAEDoIAiKMDW1hmavKZXh5jH7ttlrSlVT664FAADRgyAowmwpP+bSA3Q2Q5LVVqUt5cda7qAAAAhBBEER5tAJzwFQU9oBABCpCIIiTOe2iY038qEdAACRiiAowgxKa68Uc6I8TYQ3qW6W2KC09i15WAAAhByCoAgTG2PSzDHpkuQSCNnvzxyTHtb1gmpqDRXvPqo3dx5Q8e6jJHkDAJqEOkERKCcjRQsnZbrUCbJEQJ0g6h8BAPzFZBgGP6PdqKyslNlsls1mU3JycrAPp0kirWK0vf5R/QvW/o4WTsokEAKAKOfL9zc9QREsNsak7J4dgn0YftFY/SOT6uofjUy3hHWgBwBoOeQEISxQ/wgA4G8EQQgL1D8CAPgbQRDCAvWPAAD+RhCEsED9IwCAvxEEISxEQ/0jAEDLIghC2LDXP7KYnYe8LOZEpscDAHzGFHmElZyMFI1Mt0RU/SMAQHAQBCHsRFL9IwBA8DAcBgAAohJBEAAAiEoEQQAAICqRExSmIm1xVAAAWhpBUBgqLLFq9ppSp7W0UsyJmjkmnWniAAB4ieGwMFNYYtXUZdtdFhOtsFVp6rLtKiyxBunIAAAILwRBYaSm1tDsNaUy3Dxm3zZ7Talqat21AAAAZyMICiNbyo+59ACdzZBktVVpS/mxljsoAADCFEFQGDl0wnMA1JR2AABEM4KgMNK5bWLjjXxoBwBANCMICiOD0torxZzosoq6nUl1s8QGpbVvycMCACAsEQSFkdgYk2aOSZckl0DIfn/mmHTqBQEA4AWCoDCTk5GihZMyZTE7D3lZzIlaOCmTOkEAAHiJYolhKCcjRSPTLVSMBgCgGQiCwlRsjEnZPTsE+zAAAAhbDIcBAICoRBAEAACiEkEQAACISi0SBC1YsEBpaWlKTExUVlaWPvjggwbbb9iwQVlZWUpMTNQFF1ygF154waXNypUrlZ6eroSEBKWnp2vVqlVOj7///vsaM2aMUlNTZTKZ9MYbb/jzLQEAgDAX8CBoxYoVysvL08MPP6wdO3bo0ksv1VVXXaW9e/e6bV9eXq6rr75al156qXbs2KHf/va3uvfee7Vy5UpHm+LiYk2YMEG5ubn65JNPlJubq/Hjx+ujjz5ytPnhhx/0s5/9TPPnzw/0WwQAAGHIZBhGQJccHzx4sDIzM7Vw4ULHtr59+2rcuHGaN2+eS/vp06dr9erVKisrc2ybMmWKPvnkExUXF0uSJkyYoMrKSr399tuONjk5OWrXrp2WL1/usk+TyaRVq1Zp3LhxXh93ZWWlzGazbDabkpOTvX4eAAAIHl++vwPaE3T69Glt27ZNo0aNcto+atQobd682e1ziouLXdqPHj1aW7duVXV1dYNtPO3TG6dOnVJlZaXTDQAARK6ABkFHjhxRTU2NunTp4rS9S5cuqqiocPuciooKt+3PnDmjI0eONNjG0z69MW/ePJnNZsetW7duTd4XAAAIfS2SGG0yOVcyNgzDZVtj7etv93WfjXnooYdks9kct3379jV5Xwi+mlpDxbuP6s2dB1S8+6hqagM66gsACEMBrRjdsWNHxcbGuvTQHDp0yKUnx85isbht36pVK3Xo0KHBNp726Y2EhAQlJCQ0+fkIHYUlVs1eUyqrrcqxLcWcqJlj0llbDQDgENCeoPj4eGVlZamoqMhpe1FRkYYOHer2OdnZ2S7t161bp4EDByouLq7BNp72iehRWGLV1GXbnQIgSaqwVWnqsu0qLLEG6cgAAKEm4GuH5efnKzc3VwMHDlR2drZeeukl7d27V1OmTJFUNwx14MAB/fWvf5VUNxNs/vz5ys/P1+TJk1VcXKxFixY5zfqaNm2aLrvsMhUUFOjaa6/Vm2++qfXr12vjxo2ONt9//72++uorx/3y8nLt3LlT7du31/nnnx/ot40gqKk1NHtNqdwNfBmSTJJmrynVyHQLi80CAAIfBE2YMEFHjx7V448/LqvVqoyMDK1du1bdu3eXJFmtVqeaQWlpaVq7dq3uu+8+Pf/880pNTdVzzz2n66+/3tFm6NCheu211/TII4/o0UcfVc+ePbVixQoNHjzY0Wbr1q36+c9/7rifn58vSfrlL3+ppUuXBvhdIxi2lB9z6QE6myHJaqvSlvJjLD4LAAh8naBwRZ2g8PPmzgOa9trORtv9aWJ/Xdv/vMAfEACgxYVMnSCgJXVum+jXdgCAyEYQhIgxKK29UsyJ8pTtY1LdLLFBae1b8rAAACGKIAgRIzbGpJlj0iXJJRCy3585Jp2kaACAJIIgRJicjBQtnJQpi9l5yMtiTtTCSZnUCQKAZvCmEK2/2rSEgM8OA1paTkaKRqZbtKX8mA6dqFLntnVDYPQAAUDTeVOI1l9tWgqzwzxgdhgAAHXshWjrBwz2n5YLJ2VKkl/aNDcQ8uX7myDIA4IgAECkqKk1Gu0d99SmptbQJQXveKzDZpLUJTlBkkkVlc1rYzEnauP0K5rVc+/L9zfDYQAARLDmDlGZW8c3Woi2ovJUg8fgbZuWLmhLEAQAQITyNIxlX0+xoSEqe5tfD+vREofqcOiE54DL3wiCAAAIYw0NYzW2nuKs1bskmRpss2rngQAevauWLGhLEAQAQIhqLJenJYaxjv1QrfZJ8Tr+w2m3wdLZ+T7fVlY1q42lhQvaEgSFIG8S2AAAka2xXJ7Ghrr8OYw1rn+qlmzaI5Pk9Hr2b6ZZY38iqW5YrTltWrqgLbPDPAjW7LBQqp8AAAiOxqakP3/zAM15q6zBGVvtkuJ07IdqvxzP8slDZDt5OizqBDFF3g+CEQR5U4eBQAgAQl9zevS9mZLubYDjj2Gss6etN2eqva9tmoop8mHImwS22WtKNTLdwtAYAIQwb3s6PAUCW8qPNZrL420Pjz+Gsc4eooqNMTU6fd1fbVoCQVCI8Oaib+n6CQAA33gzJd2ez+MpUDp1ptZvxzMy3aJBae1dXstSLyhbOCmz0TaRiCAoRHhbF6El6ycAALznbY9+ba101989B0p5I3p59XqNDXXZZ1rFxpgaXU8xWtdcJAgKEd7WRWjJ+gkAAFfNGcay2qr0yJslDQZKy7fslSU5sdE8nUd/ka67/t6yw1iRhiAoRAxKa68Uc6IqbKFTPwEA4Mwfw1jHfjjt8TF77Z77RlykZ9d/2WCAk5ORooUx0TmM5S/MDvMgmLPDJPcXPbPDACB4GpvBmzeil55Z/2+/vNafJvZXQquYZiVYRyumyPsBdYIAAHa+rKTe0DCWt1Pbl08eouyeHQhwmoAp8mEsWpPTACCUeZPv480w1u+uzdCct8q8Tn2IxjydlkQQFIK46AEgtHg7M7dHxzaNTjePiTGF1NIR0YwgCAAANZxb48sM3uyeHRrs0c/JSInaujyhhiAIABD1GsvH9HUGb2M9+qQ+hIaYYB8AAACBVlNrqHj3Ub2584CKdx9VTe1/Qhn7rK/6OT/24oWFJVbFxpg0c0y6pP8MW9k1dRjLHihd2/88ZffsQAAUBPQEAQAiWkO9PCPTLV6v28gwVuQhCAIARKzG1vLKG9HLp3UbGcaKLARBAICI5M1aXks27fFqX2fPDmMGb+QgJwgAEJG8qe3z3cnGCxdKrNsYqQiCAAARydvaPue2jnNJdrYzqS5/iHUbIxNBEAAgInnbe/OrYWmS/DfrC+GDIAgAENY8TX+31/ZprJfn7isu1MJJmbKYnYMmizmRhasjHInRAICw1ViRw5lj0r1aooJZX9GJVeQ9CNYq8gAA73ia/m4PW+y9OI0FSogsrCIPAIho3kx/P7vIIb08cIcgCAAQdryZ/n52kUNq+8AdEqMBAGHH2+nv3rZDdCIIAgCEHW+nv1PkEA0hCAIAhB1vp79T5BANIQgCAISd2BiTZo5Jl0SRQzQdQRAAIGR5KoQoSTkZKRQ5RLMwOwwAEJK8qe/D9Hc0B8USPaBYYuSrqTX4wwmEKG8LIQL1USwRaAQVZIHQ5UshRH64oDnICULUsf/CrF9orcJWpanLtquwxBqkIwMg+VYIEWgOgiBElcZ+YUp1vzDPTr4E0LIohIiWQhCEqMIvTCB0eJr5RSFEtBRyghBV+IUJhIaG8vJGpluUYk5Uha3Kba+tSXXT4CmEiOaiJwhRhV+YQPA1lpdXVFpBIUS0CIIgRBVK7QPB5W1e3sh0C4UQEXAMhyGq2EvtT122XSbJ6Q8xvzCBwPMlL49CiAg0giBEHXup/fr5CBbqBAEB52teXmyMSdk9OwTykBDFCIIQlfiFCQQHeXkIJQRBiFr8wgRanj0vj5lfCAUkRgMAWow9L09i5heCjyAIANCi7Hl5zPxCsDEcBgDwu5pao8GcO/LyEAoIggAAftVQNeize3nIy0OwMRwGAPCbxqpBF5ZYg3RkgCuCIACAX3hbDdq+UCoQbARBAAC/8KUaNBAKCIIAAH7hazVoINgIggAAfkE1aIQbgiAAgF/Yq0F7muRuUt0sMapBI1QQBAEA/IJq0Ag3LRIELViwQGlpaUpMTFRWVpY++OCDBttv2LBBWVlZSkxM1AUXXKAXXnjBpc3KlSuVnp6uhIQEpaena9WqVc1+3ZZQU2uoePdRvbnzgIp3H2WWRIjj8wJ8QzVohJOAF0tcsWKF8vLytGDBAg0bNkwvvviirrrqKpWWlur88893aV9eXq6rr75akydP1rJly7Rp0ybdeeed6tSpk66//npJUnFxsSZMmKA5c+bouuuu06pVqzR+/Hht3LhRgwcPbtLrtgRvC4ghNPB5AU1DNWiEC5NhGAH9aTt48GBlZmZq4cKFjm19+/bVuHHjNG/ePJf206dP1+rVq1VWVubYNmXKFH3yyScqLi6WJE2YMEGVlZV6++23HW1ycnLUrl07LV++vEmvW19lZaXMZrNsNpuSk5N9f+P12AuI1T/Z9j8J/EIKLXxeABCefPn+Duhw2OnTp7Vt2zaNGjXKafuoUaO0efNmt88pLi52aT969Ght3bpV1dXVDbax77MprxtIFBALL3xeQMMYJkakCOhw2JEjR1RTU6MuXbo4be/SpYsqKircPqeiosJt+zNnzujIkSNKSUnx2Ma+z6a87qlTp3Tq1CnH/crKSu/epBd8KSDGOjrBx+cFeMYwMSJJiyRGm0zO48CGYbhsa6x9/e3e7NOX1503b57MZrPj1q1bN4/H5ysKiIUXPi/APdYFQ6QJaBDUsWNHxcbGuvS+HDp0yKWXxs5isbht36pVK3Xo0KHBNvZ9NuV1H3roIdlsNsdt37593r/RRlBALLzweQGuGCZGJApoEBQfH6+srCwVFRU5bS8qKtLQoUPdPic7O9ul/bp16zRw4EDFxcU12Ma+z6a8bkJCgpKTk51u/kIBsfDC5wW4Yl0wRKKAD4fl5+frlVde0eLFi1VWVqb77rtPe/fu1ZQpUyTV9cDccsstjvZTpkzRN998o/z8fJWVlWnx4sVatGiRHnjgAUebadOmad26dSooKNDnn3+ugoICrV+/Xnl5eV6/bkuigFh44fNCNPOU9MwwMSJRwOsETZgwQUePHtXjjz8uq9WqjIwMrV27Vt27d5ckWa1W7d2719E+LS1Na9eu1X333afnn39eqampeu655xw1giRp6NCheu211/TII4/o0UcfVc+ePbVixQpHjSBvXrel2QuI1U8otJBQGJL4vBCNGkp6ZpgYkSjgdYLClb/rBNnV1BoUEAsjfF6IFo3Vxnr+5gGa81aZKmxVbvOCTKr7kbBx+hX8H0FQ+fL9HfCeIDiLjTExrTqM8HkhGjSW9GySNOetMj36i3Td9fftMklObRkmRrhiAVUAiHLeJj23S4pnXTBEFHqCACDK+ZL0fG3/81gXDBGDIAgAopyvSc8MEyNSMBwGAFGO2liIVgRBABDlqI2FaEUQBABw1MYi6RnRhJwgAICkukCIpGdEE4IgAIADSc+IJgyHAQCAqEQQBAAAohJBEAAAiEoEQQAAICoRBAEAgKhEEAQAAKISQRAAAIhK1AkCgChRU2tQCBE4C0EQAESBwhKrZq8pldVW5diWYk7UzDHpLImBqMVwGABEuMISq6Yu2+4UAElSha1KU5dtV2GJNUhHBgQXQRAARLCaWkOz15TKcPOYfdvsNaWqqXXXAohsBEEAEMG2lB9z6QE6myHJaqvSlvJjLXdQQIggCAKACHbohOcAqCntgEhCEAQAEaxz20S/tgMiCUEQAESwQWntlWJOlKeJ8CbVzRIblNa+JQ8LCAkEQQAQwWJjTJo5Jl2SXAIh+/2ZY9KpF4SoRBAEABGgptZQ8e6jenPnARXvPuo02ysnI0ULJ2XKYnYe8rKYE7VwUiZ1ghC1KJYIAGHOm0KIORkpGpluoWI0cBaTYRgUh3CjsrJSZrNZNptNycnJwT4cAHDLXgix/h9ye2hDTw+ijS/f3wyHAUCYohAi0DwEQQAQpiiECDQPQRAAhCkKIQLNQxAEAGGKQohA8xAEAUCYohAi0DwEQQAQpiiECDQPQRAAhDEKIQJNR7FEAAhzFEIEmoYgCABCXE2t0WiAExtjUnbPDkE6QiA8EQQBQAjzZkkMAE1DThAAhCj7khj1CyJW2Ko0ddl2FZZYg3RkQGQgCAKAEMSSGEDgEQQBQAhiSQwg8AiCACAEsSQGEHgEQQAQglgSAwg8giAACEEsiQEEHkEQAIQglsQAAo8gCABCFEtiAIFFsUSgmbyp5gs0FUtiAIFDEAQ0A9V80RJYEgMIDIbDgCaimi8AhDeCIKAJqOYLAOGPIAhoAqr5wl9qag0V7z6qN3ceUPHuowTOQAsiJwhoAqr5wh/IKQOCi54goAmo5ovmIqcMCD6CIKAJqOaL5iCnDAgNBEFAE1DNF81BThkQGgiCgCaimi+aipwyIDSQGA00A9V80RTklAGhgSAIaCaq+cJX9pyyCluV27wgk+p6FMkpAwKL4TCgBVALBmcjpwwIDfQEAQFGLRi4Y88pq39tWLg2gBZjMgyDn6RuVFZWymw2y2azKTk5OdiHgzBlrwVT/z+Z/fc9CdSoqTXIKQP8yJfvb3qCgABprBaMSXW1YEamW/jSi2LklAHBQ04QECDUggGA0EYQBAQItWAAILQRBAEBQi0YAAht5AQBAUItGJD0DIQ2giAgQOy1YKYu2y6T5BQIUQsm8lEaAQh9AR0OO378uHJzc2U2m2U2m5Wbm6vvvvuuwecYhqFZs2YpNTVVrVu31uWXX65du3Y5tTl16pTuuecedezYUUlJSRo7dqz279/v1OaJJ57Q0KFD1aZNG5177rl+fmeAd1hfLDrZSyPUT4yvsFVp6rLtKiyxBunIAJwtoHWCrrrqKu3fv18vvfSSJOk3v/mNevTooTVr1nh8TkFBgZ544gktXbpUF110kX73u9/p/fff1xdffKG2bdtKkqZOnao1a9Zo6dKl6tChg+6//34dO3ZM27ZtU2xsrCRp5syZOvfcc7V//34tWrSo0eCrPuoEwZ8YFokeNbWGLil4x+PMQPsw6MbpV3ANAAHgy/d3wIKgsrIypaen68MPP9TgwYMlSR9++KGys7P1+eefq3fv3i7PMQxDqampysvL0/Tp0yXV9fp06dJFBQUFuuOOO2Sz2dSpUyf97W9/04QJEyRJBw8eVLdu3bR27VqNHj3aaZ9Lly5VXl4eQRCAFlG8+6huevnDRtstnzyE+kBAAPjy/R2w4bDi4mKZzWZHACRJQ4YMkdls1ubNm90+p7y8XBUVFRo1apRjW0JCgoYPH+54zrZt21RdXe3UJjU1VRkZGR73641Tp06psrLS6QYAvqI0AhA+AhYEVVRUqHPnzi7bO3furIqKCo/PkaQuXbo4be/SpYvjsYqKCsXHx6tdu3Ye2zTFvHnzHLlLZrNZ3bp1a/K+AEQvSiMA4cPnIGjWrFkymUwN3rZu3SpJMplcx7sNw3C7/Wz1H/fmOd60achDDz0km83muO3bt6/J+wIQveylETz9NTKpbpYYpRGA4PN5ivzdd9+tiRMnNtimR48e+vTTT/Xtt9+6PHb48GGXnh47i8Uiqa63JyXlP7NmDh065HiOxWLR6dOndfz4cafeoEOHDmno0KG+vh2HhIQEJSQkNPn5ACBRGgEIJz73BHXs2FF9+vRp8JaYmKjs7GzZbDZt2bLF8dyPPvpINpvNY7CSlpYmi8WioqIix7bTp09rw4YNjudkZWUpLi7OqY3ValVJSUmzgiAA8BdKIwDhIWDFEvv27aucnBxNnjxZL774oqS6KfLXXHON08ywPn36aN68ebruuutkMpmUl5enuXPnqlevXurVq5fmzp2rNm3a6Oabb5Ykmc1m3Xbbbbr//vvVoUMHtW/fXg888ID69eunESNGOPa7d+9eHTt2THv37lVNTY127twpSbrwwgt1zjnnBOptA4CkukBoZLqF0ghACAtoxehXX31V9957r2Mm19ixYzV//nynNl988YVsNpvj/oMPPqiTJ0/qzjvv1PHjxzV48GCtW7fOUSNIkp555hm1atVK48eP18mTJ3XllVdq6dKljhpBkvTYY4/pL3/5i+P+gAEDJEnvvvuuLr/88kC8XQBwEhtjYho8EMICWiwxnFEnCACA8BMSdYIAAABCGQuoAkATsBQKEP4IggDAR6wQD0QGhsMAwAesEA9EDoIgAPBSTa2h2WtK5W42iX3b7DWlqqllvgkQDgiCAMBLW8qPufQAnc2QZLVVaUv5sZY7KABNRhAEAF5ihXggshAEAYCXWCEeiCwEQQDgJVaIByILQRAAeMm+Qrwkl0CIFeKB8EMQBAA+YIV4IHJQLBEAfMQK8UBkIAgCgCZghXgg/DEcBgAAohJBEAAAiEoEQQAAICqREwQA9dTUGiQ9A1GAIAgAzlJYYtXsNaVOa4SlmBM1c0w609+BCMNwGAD8n8ISq6Yu2+6ySGqFrUpTl21XYYk1SEcGIBAIggBAdUNgs9eUynDzmH3b7DWlqql11wJAOCIIAgBJW8qPufQAnc2QZLVVaUv5sZY7KAABRU4QECJIxg2uQyc8B0BNaQcg9BEEASGAZNzg69w2sfFGPrQDEPoYDgOCjGTc0DAorb1SzIkuq8PbmVQXmA5Ka9+ShwUggAiCgCAiGTd0xMaYNHNMuiS5BEL2+zPHpDNECUQQgiAgiEjGDS05GSlaOClTFrPzkJfFnKiFkzIZmgQiDDlBQBCRjBt6cjJSNDLdQpI6EAUIgoAgIhk3NMXGmJTds0OwDwNAgDEcBgQRybgAEDwEQUAQkYwLAMFDEAQEGcm4Laum1lDx7qN6c+cBFe8+ysw7IIqREwSEAJJxWwZFKQGczWQYBj+D3KisrJTZbJbNZlNycnKwDwdAM9mLUtb/g2cPM+l1AyKDL9/fDIcBiHgUpQTgDkEQgIhHUUoA7hAEAYh4FKUE4A5BEICIR1FKAO4QBAGIeBSlBOAOQRCAiEdRSgDuEAQBiAoUpQRQH8USAUQNilICOBtBEICowgrxAOwYDgMAAFGJIAgAAEQlhsOAMFJTa5DPAgB+QhAEhAlWQAcA/2I4DAgD9hXQ669/VWGr0tRl21VYYg3SkQFA+CIIAkIcK6B7r6bWUPHuo3pz5wEV7z7KOQHQIIbDgBDnywro0Tz1m+FCAL6iJwgIcayA3jiGCwE0BUEQEOJYAb1hDBcCaCqCICDEsQJ6w3wZLgSAsxEEASHO1xXQoy05mOFCAE1FYjQQBuwroNdP/LXUS/yNxuRghgsBNBVBEBAmGlsB3Z4cXL/fx54cvHBSZkQGQvbhwgpbldu8IJPqgsVoHS4E4BnDYUAYsa+Afm3/85Tds4PTEFikJwd7GubzdbgQAOzoCQIiQKTXEmpsmM/b4UIAOBtBEBABIjk52NthvsaGCwGgPoIgIAJEanJwY8N8JtUN841Mtyg2xuQYLgQAb5ATBESASK0lRA0gAIFEEAREgEhNDo7kYT4AwUcQBEQIe3Kwxew85GUxJ4bt9PhIHeYDEBrICQIiSKQlB1MDCEAgEQQBESaSkoPtw3xTl22XSXIKhMJ5mA9AaGA4DEDQNbTeWSQO8wEIDfQEAQgqb9Y7i7RhPgChIaA9QcePH1dubq7MZrPMZrNyc3P13XffNfgcwzA0a9YspaamqnXr1rr88su1a9cupzanTp3SPffco44dOyopKUljx47V/v37HY/v2bNHt912m9LS0tS6dWv17NlTM2fO1OnTpwPxNgE0kb0QYv1p8PZCiIUlVsc2T0uGAEBTBTQIuvnmm7Vz504VFhaqsLBQO3fuVG5uboPPefLJJ/X0009r/vz5+vjjj2WxWDRy5EidOHHC0SYvL0+rVq3Sa6+9po0bN+r777/XNddco5qaGknS559/rtraWr344ovatWuXnnnmGb3wwgv67W9/G8i3C8AH0bDeGYDQZjIMIyB/YcrKypSenq4PP/xQgwcPliR9+OGHys7O1ueff67evXu7PMcwDKWmpiovL0/Tp0+XVNfr06VLFxUUFOiOO+6QzWZTp06d9Le//U0TJkyQJB08eFDdunXT2rVrNXr0aLfH84c//EELFy7U119/7dXxV1ZWymw2y2azKTk5uSmnAAhZNbVG0IeWincf1U0vf9hou+WTh0RMojeAwPPl+ztgOUHFxcUym82OAEiShgwZIrPZrM2bN7sNgsrLy1VRUaFRo0Y5tiUkJGj48OHavHmz7rjjDm3btk3V1dVObVJTU5WRkaHNmzd7DIJsNpvat/c8jfbUqVM6deqU435lZaVP7xcIF97k4LQECiECCLaADYdVVFSoc+fOLts7d+6siooKj8+RpC5dujht79Kli+OxiooKxcfHq127dh7b1Ld79279+c9/1pQpUzwe77x58xy5S2azWd26dfP85oAw5UsOjr94mvlFIUQAweZzEDRr1iyZTKYGb1u3bpUkmUyu3euGYbjdfrb6j3vzHE9tDh48qJycHN144426/fbbPT7/oYceks1mc9z27dvX4OsB4SYYOTiFJVZdUvCObnr5Q017baduevlDXVLwjgpLrBG73hmA8OHzcNjdd9+tiRMnNtimR48e+vTTT/Xtt9+6PHb48GGXnh47i8Uiqa63JyXlP93yhw4dcjzHYrHo9OnTOn78uFNv0KFDhzR06FCn/R08eFA///nPlZ2drZdeeqnBY05ISFBCQkKDbYBw5stipNk9OzQ7b8je61Q/pLL3Oi2clEkhRABB5XMQ1LFjR3Xs2LHRdtnZ2bLZbNqyZYsGDRokSfroo49ks9lcghW7tLQ0WSwWFRUVacCAAZKk06dPa8OGDSooKJAkZWVlKS4uTkVFRRo/frwkyWq1qqSkRE8++aRjXwcOHNDPf/5zZWVlacmSJYqJoS4kopsvOTjNzRtqrNfJpLpep43Tr9DCSZkur2UJQo4SgOgTsMTovn37KicnR5MnT9aLL74oSfrNb36ja665xikpuk+fPpo3b56uu+46mUwm5eXlae7cuerVq5d69eqluXPnqk2bNrr55pslSWazWbfddpvuv/9+dejQQe3bt9cDDzygfv36acSIEZLqeoAuv/xynX/++Xrqqad0+PBhx+vZe5uAaONtbs2eIz/q2fVfNtiD01hw4kuvE4UQAQRLQCtGv/rqq7r33nsdM7nGjh2r+fPnO7X54osvZLPZHPcffPBBnTx5UnfeeaeOHz+uwYMHa926dWrbtq2jzTPPPKNWrVpp/PjxOnnypK688kotXbpUsbGxkqR169bpq6++0ldffaWuXbs6vV6AKgIAIc+bxUi7JCdo+Za9jfbgjEy3NBik+DrzK5LWOwMQPgJWJyjcUScIkciepyO5z8HJG9FLz6z/d6P7aax2DzWAAASLL9/fJMoAUaSxxUh7dEzyaj+N9fQw8wtAOGABVSDKNJSDU7z7qFf7aCy/KDbGxMwvACGPniAgCnlajNSfPTiN9Tox8wtAsNETBMDB3z04zPwCEMpIjPaAxGhEM2/rBIXCQqwAcLaQWEAVQPjypgcnVBZiBYCmoifIA3qCAM88LYlhD5HI+QEQLEyRBxAwwViIFQACgSAIgE98WRIDAEIZQRAAn/i6JAYAhCqCIAA+8XYhVm/bAUCwEAQB8AlLYgCIFARBAHxiL6goySUQYkkMAOGEIAiAz1gSA0AkoFgigCZhSQwA4Y4gCECT2RdiBYBwxHAYAACISgRBAAAgKhEEAQCAqEQQBAAAohJBEAAAiEoEQQAAICoRBAEAgKhEEAQAAKISQRAAAIhKVIz2wDAMSVJlZWWQjwQAAHjL/r1t/x5vCEGQBydOnJAkdevWLchHAgAAfHXixAmZzeYG25gMb0KlKFRbW6uDBw+qbdu2Mpn8uyBkZWWlunXrpn379ik5Odmv+8Z/cJ5bBue5ZXCeWwbnueUE6lwbhqETJ04oNTVVMTENZ/3QE+RBTEyMunbtGtDXSE5O5j9ZC+A8twzOc8vgPLcMznPLCcS5bqwHyI7EaAAAEJUIggAAQFQiCAqChIQEzZw5UwkJCcE+lIjGeW4ZnOeWwXluGZznlhMK55rEaAAAEJXoCQIAAFGJIAgAAEQlgiAAABCVCIIAAEBUIgjygwULFigtLU2JiYnKysrSBx984LHte++9J5PJ5HL7/PPPndqtXLlS6enpSkhIUHp6ulatWhXotxHy/H2ely5d6rZNVVVVS7ydkObLuZakU6dO6eGHH1b37t2VkJCgnj17avHixU5tuKZd+fs8c02758t5vvXWW92ew5/85CdO7bieXfn7PLfI9WygWV577TUjLi7OePnll43S0lJj2rRpRlJSkvHNN9+4bf/uu+8akowvvvjCsFqtjtuZM2ccbTZv3mzExsYac+fONcrKyoy5c+carVq1Mj788MOWelshJxDnecmSJUZycrLT41artaXeUsjy9VwbhmGMHTvWGDx4sFFUVGSUl5cbH330kbFp0ybH41zTrgJxnrmmXfl6nr/77junc7dv3z6jffv2xsyZMx1tuJ5dBeI8t8T1TBDUTIMGDTKmTJnitK1Pnz7GjBkz3La3fzkfP37c4z7Hjx9v5OTkOG0bPXq0MXHixGYfb7gKxHlesmSJYTab/XiUkcHXc/32228bZrPZOHr0qMd9ck27CsR55pp25et5rm/VqlWGyWQy9uzZ49jG9ewqEOe5Ja5nhsOa4fTp09q2bZtGjRrltH3UqFHavHlzg88dMGCAUlJSdOWVV+rdd991eqy4uNhln6NHj250n5EqUOdZkr7//nt1795dXbt21TXXXKMdO3b49djDTVPO9erVqzVw4EA9+eSTOu+883TRRRfpgQce0MmTJx1tuKadBeo8S1zTZ2vO3w67RYsWacSIEerevbtjG9ezs0CdZynw1zMLqDbDkSNHVFNToy5dujht79KliyoqKtw+JyUlRS+99JKysrJ06tQp/e1vf9OVV16p9957T5dddpkkqaKiwqd9RrpAnec+ffpo6dKl6tevnyorK/WnP/1Jw4YN0yeffKJevXoF/H2Foqac66+//lobN25UYmKiVq1apSNHjujOO+/UsWPHHPkqXNPOAnWeuaadNeU8n81qtertt9/W3//+d6ftXM/OAnWeW+J6JgjyA5PJ5HTfMAyXbXa9e/dW7969Hfezs7O1b98+PfXUU44vZ1/3GS38fZ6HDBmiIUOGONoMGzZMmZmZ+vOf/6znnnsuAO8gfPhyrmtra2UymfTqq686Vm5++umndcMNN+j5559X69atfd5ntPD3eeaadq+p197SpUt17rnnaty4cX7bZyTz93luieuZ4bBm6Nixo2JjY10i3UOHDrlExA0ZMmSI/v3vfzvuWyyWZu8zkgTqPNcXExOjiy++uME2ka4p5zolJUXnnXee44tZkvr27SvDMLR//35JXNP1Beo81xft13Rz/nYYhqHFixcrNzdX8fHxTo9xPTsL1HmuLxDXM0FQM8THxysrK0tFRUVO24uKijR06FCv97Njxw6lpKQ47mdnZ7vsc926dT7tM5IE6jzXZxiGdu7c2WCbSNeUcz1s2DAdPHhQ33//vWPbl19+qZiYGHXt2lUS13R9gTrP9UX7Nd2cvx0bNmzQV199pdtuu83lMa5nZ4E6z/UF5HoOaNp1FLBPC1y0aJFRWlpq5OXlGUlJSY4M9xkzZhi5ubmO9s8884yxatUq48svvzRKSkqMGTNmGJKMlStXOtps2rTJiI2NNX7/+98bZWVlxu9//3umXwbgPM+aNcsoLCw0du/ebezYscP41a9+ZbRq1cr46KOPWvz9hRJfz/WJEyeMrl27GjfccIOxa9cuY8OGDUavXr2M22+/3dGGa9pVIM4z17QrX8+z3aRJk4zBgwe73SfXs6tAnOeWuJ4Jgvzg+eefN7p3727Ex8cbmZmZxoYNGxyP/fKXvzSGDx/uuF9QUGD07NnTSExMNNq1a2dccsklxltvveWyz//5n/8xevfubcTFxRl9+vRx+vKOVv4+z3l5ecb5559vxMfHG506dTJGjRplbN68uaXeTkjz5VwbhmGUlZUZI0aMMFq3bm107drVyM/PN3788UenNlzTrvx9nrmm3fP1PH/33XdG69atjZdeesnjPrmeXfn7PLfE9WwyDMPwX78SAABAeCAnCAAARCWCIAAAEJUIggAAQFQiCAIAAFGJIAgAAEQlgiAAABCVCIIAAEBUIggCAABRiSAIAABEJYIgAAAQlQiCAABAVCIIAgAAUen/Aw7ISacMC3DYAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "voteLogits = [math.log(v/(1-v)) for v in tableVotes]\n",
    "\n",
    "nu, nuSigma = 3.8, 0.221  #7, 0.24\n",
    "nuSeatLogits = [t.cdf(xx,nu,0,nuSigma) for xx in voteLogits]\n",
    "nuSeats = [nSL for nSL in nuSeatLogits]\n",
    "#plt.plot(tableVotes,nuSeats,label=\"nu=\"+str(nu)+\", nuSigma=\"+str(nuSigma))\n",
    "#plt.scatter(tableVotes, tableSeats,label=\"Cory\")\n",
    "tRows = len(tableVotes)\n",
    "offSet = [nuSeats[i] - tableSeats[i] for i in range(tRows) ]\n",
    "rmse = (np.sum([(nuSeats[i] - tableSeats[i])**2 for i in range(tRows)]) / tRows )**0.5\n",
    "plt.scatter(tableVotes,offSet, label=\"offSet\"+str(r3(np.sum(offSet)))+\" rmse\"+str(r5(rmse)) )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52dc7816-8136-468c-a001-6be5c41b01ce",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
